Deck 4: Exponential Functions

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Question
In the exponential formula Q=47,200(0.9)tQ=47,200(0.9)^{t} , if Q=a(1+r)tQ=a(1+r)^{t} then r=%r=\ldots \% .
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Question
In 2006, the cost of a particular piece of computer equipment was $490\$ 490 and going down at a rate of 14%14 \% per year. Assuming this percentage remains constant, what is the formula for CC , the cost of this equipment in dollars, as a function of tt , the number of years since 2006 ?

A) C=490(0.86)t C=490(0.86)^{t}
B) C=490(1.14)t C=490(-1.14)^{t}
C) C=490(0.14)t C=490(0.14)^{t}
D) C=490(0.86)t C=490(-0.86)^{t}
Question
If you start with $8,000\$ 8,000 , how much money will you have after a 10%10 \% increase?
Question
If you start with $6,000\$ 6,000 , how much money will you have after a 5%5 \% increase followed by a 25%25 \% decrease?
Question
Which of the graphs in the following figure is the graph of 150(1.1)t150(1.1)^{t} ?
 Which of the graphs in the following figure is the graph of  150(1.1)^{t}  ?  <div style=padding-top: 35px>
Question
What is the growth factor if sales increase by 37%37 \% each month?
Question
The populations of 4 species of animals are given by the following equations:
P1=650(0.71)tP2=600(1.2)tP3=270(0.88)tP4=610(1.05)tP_{1}=650(0.71)^{t} P_{2}=600(1.2)^{t} P_{3}=270(0.88)^{t} P_{4}=610(1.05)^{t}
Which species are shrinking in size?

A) P4P_{4}
B) P3P_{3}
C) P2P_{2}
D) P1P_{1}
Question
The populations of 4 species of animals are given by the following equations:
P1=470(0.81)tP2=900(1.28)tP3=670(0.73)tP4=640(1.05)tP_{1}=470(0.81)^{t} P_{2}=900(1.28)^{t} P_{3}=670(0.73)^{t} P_{4}=640(1.05)^{t}
What is the annual percent growth rate for the population that is growing the fastest?
Question
The populations of 4 species of animals are given by the following equations:
P1=390(0.75)tP2=100(1.09)tP3=230(0.82)tP4=600(1.05)tP_{1}=390(0.75)^{t} P_{2}=100(1.09)^{t} P_{3}=230(0.82)^{t} P_{4}=600(1.05)^{t}
What is the largest initial population of the 4 species?
Question
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.38%1.38 \% per year. How many million people would you expect to live in the United States in the year 2020? Round to 1 decimal place.
Question
A quantity decreased from 100 to 95 . By what percentage did it decrease?
Question
A store's sales of cassette tapes of music decreased by 6%6 \% per year over a period of 5 years. By what total percent did sales of cassette tapes decrease over this time period? Round to 1 decimal place.
Question
The population of a city has been growing at a rate of 4%4 \% per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.
Question
In some developing countries, the inflation rate has been as high as 0.94%0.94 \% per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.
Question
The price of an item increases due to inflation. Let p(t)=22.50(1.037)tp(t)=22.50(1.037)^{t} be the price of the item as a function of time in years, with t=0t=0 in 2004. What is the weekly inflation rate? Round to 2 decimal places.
Question
The price of an item increases due to inflation. Let p(t)=22.50(1.029)tp(t)=22.50(1.029)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004. What is the practical interpretation of p1(70)p^{-1}(70) ?

A) The price in 2004 of an item that is $70\$ 70 now.
B) The price now of an item that was $70 in 2004.
C) The time at which the price reaches $70\$ 70 .
D) The price of the item after 70 years.
Question
The amount of pollution in a harbor tt hours after it was contaminated by illegal dumping is given by A=70(0.65)tA=70(0.65)^{t} tons. What percentage of the pollution leaves the harbor each hour?
Question
A radioactive substance decays by 12%12 \% every year. Which of the following is the formula for the quantity, QQ , of a 10 gram sample remaining after tt years?

A) Q=10(0.88)tQ=10(0.88)^{t}
B) Q=10(1.12)tQ=10(1.12)^{t}
C) Q=10(1.12)tQ=10(-1.12)^{t}
D) Q=10(0.88)tQ=10(-0.88)^{t}
Question
Which equation has a rate of change of 9%9 \% ?

A) Q=(3,200)0.91tQ=(3,200) 0.91^{t}
B) Q=(3,200)109tQ=(3,200) 109^{t}
C) Q=(3,200)1.09t Q=(3,200) 1.09^{t}
D) Q=(3,200)91tQ=(3,200) 91^{t}
Question
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-1(0.8)^{x}  B)  y=1(0.8)^{x}  C)  y=1(1.2)^{-x}  D)  y=1(1.2)^{x}  <div style=padding-top: 35px>

A) y=1(0.8)xy=-1(0.8)^{x}
B) y=1(0.8)xy=1(0.8)^{x}
C) y=1(1.2)xy=1(1.2)^{-x}
D) y=1(1.2)xy=1(1.2)^{x}
Question
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-4(1.1)^{x}  B)  y=4(1.1)^{x}  C)  y=4(0.9)^{-x}  D)  y=4(0.9)^{x}  <div style=padding-top: 35px>

A) y=4(1.1)xy=-4(1.1)^{x}
B) y=4(1.1)xy=4(1.1)^{x}
C) y=4(0.9)xy=4(0.9)^{-x}
D) y=4(0.9)xy=4(0.9)^{x}
Question
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-4(1.1)^{x}  B)  y=4(1.1)^{x}  C)  y=4(0.9)^{-x}  D)  y=4(0.9)^{x}  <div style=padding-top: 35px>

A) y=4(1.1)xy=-4(1.1)^{x}
B) y=4(1.1)xy=4(1.1)^{x}
C) y=4(0.9)xy=4(0.9)^{-x}
D) y=4(0.9)xy=4(0.9)^{x}
Question
Which of the following formulas are exponential?

A) P(t)=8.9(1.21)t P(t)=8.9(1.21)^{t}
B) P(t)=1.899.68t P(t)=1.89-9.68 t
C) P(t)=17.8t+40.05t22.25 P(t)=17.8^{t}+40.05 t-22.25
D) P(t)=(1.4641)t2670 P(t)=(1.4641)^{t} 2670
E) P(t)=178e2.42t P(t)=178 e^{2.42 t}
F) P(t)=1.78e0.605t P(t)=1.78 e^{-0.605 t}
G) P(t)=(4.45+12.1t)t P(t)=(4.45+12.1 t)^{t}
Question
The average life expectancy in a country tends to increase by the same percentage each year. Should a linear or an exponential function be used to model this scenario?
Question
The following table gives values from an exponential or a linear function. Determine which, and find values for aa and bb so that f(x)=a+bxf(x)=a+b x if the function is linear, or f(x)=a(b)xf(x)=a(b)^{x} if the function is exponential.
a= ---------------,b= ------------
 The following table gives values from an exponential or a linear function. Determine which, and find values for  a  and  b  so that  f(x)=a+b x  if the function is linear, or  f(x)=a(b)^{x}  if the function is exponential. a= ---------------,b= ------------  <div style=padding-top: 35px>
Question
The table below shows vv , the dollar value of a share of a certain stock, as a function of tt , the time (in weeks) since the initial offering of the stock. A possible formula for v(t)v(t) is v(t)=()tv(t)=\ldots(\ldots)^{t} . Round the second answer to 3 decimal places.
 The table below shows  v , the dollar value of a share of a certain stock, as a function of  t , the time (in weeks) since the initial offering of the stock. A possible formula for  v(t)  is  v(t)=\ldots(\ldots)^{t} . Round the second answer to 3 decimal places.  <div style=padding-top: 35px>
Question
A population has size 3,500 at time t=0t=0 , with tt in years. If the population grows by 80 people per year, what is the formula for PP , the population at time tt ?

A) P=3,500(1.8)t P=3,500(1.8) t
B) P=3,500+80t P=3,500+80 t
C) P=3,500(0.8)t P=3,500(0.8)^{t}
D) P=3,500(1.8)t P=3,500(1.8)^{t}
Question
A population has size 3,000 at time t=0t=0 , with tt in years. If the population grows by 10%10 \% per year, what is the formula for PP , the population at time tt ?

A) P=3,000(1.1)t P=3,000(1.1) t
B) P=3,000+10t P=3,000+10 t
C) P=3,000(1.1)t P=3,000(1.1)^{t}
D) P=3,000(0.1)t P=3,000(0.1)^{t}
Question
The graph below shows the quantity of a drug in a patient's bloodstream over a period of time tt , in minutes.
 <strong>The graph below shows the quantity of a drug in a patient's bloodstream over a period of time  t , in minutes.   Which of the following scenarios best describes the graph?</strong> A) The drug is injected over a 10 minute interval, during which the quantity increases linearly. After the 10 minutes, the injection is discontinued and the quantity then decays exponentially. B) The drug is injected over a 10 minute interval, during which the quantity increases exponentially. After the 10 minutes, the injection is discontinued and the quantity then decays linearly. C) The drug is injected all at once. The quantity first increases and then decreases linearly. D) The drug is injected all at once. The quantity first increases and then decreases exponentially. <div style=padding-top: 35px>
Which of the following scenarios best describes the graph?

A) The drug is injected over a 10 minute interval, during which the quantity increases linearly. After the 10 minutes, the injection is discontinued and the quantity then decays exponentially.
B) The drug is injected over a 10 minute interval, during which the quantity increases exponentially. After the 10 minutes, the injection is discontinued and the quantity then decays linearly.
C) The drug is injected all at once. The quantity first increases and then decreases linearly.
D) The drug is injected all at once. The quantity first increases and then decreases exponentially.
Question
Kevin buys a new CD player for $300\$ 300 , and finds two years later when he wants to sell it that it is only worth $82\$ 82 . Assuming the value of the CD player decreases exponentially, the formula for V(t)V(t) , the value of the CD player after tt years, is given by V(t)=()tV(t)=\ldots(\ldots)^{t} . Round your second answer to 2 decimal places.
Question
A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 15 hours after the spill. She sets up a possible model to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 6 tons\hour. She estimates that the lake will be free from the contaminant 35 hours after the spill. How many tons of the contaminant were in the lake at the 15 hour reading?
Question
A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 3 tons\hour. Using this model, she estimates that the lake will be free from the contaminant 20 hours after the spill. Thus, Q(2)= ---------- and Q(11)= ----------- The second model assumes that the amount of contaminant decreases exponentially. In this model, she finds that Q(t)=()tQ(t)=\ldots(\ldots)^{t} . Round both answers to 3 decimal places.
Question
A biologist measures the amount of contaminant in a lake 3 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 7 tons\hour. Using this model, she estimates that the lake will be free from the contaminant 24 hours after the spill. The second model assumes that the amount of contaminant decreases exponentially. She measures the spill a third time after 23 hours and finds that 44 tons remain. Which model seems best?

A) The linear one
B) The exponential one
Question
Let f(x)f(x) be given in the table below. Find the value of kk if f(x)f(x) is linear.
 Let  f(x)  be given in the table below. Find the value of  k  if  f(x)  is linear.  <div style=padding-top: 35px>
Question
Let f(x)f(x) be given in the table below. Find the value of kk if f(x)f(x) is exponential.
 Let  f(x)  be given in the table below. Find the value of  k  if  f(x)  is exponential.  <div style=padding-top: 35px>
Question
The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is g(x)=()xg(x)=\ldots(\ldots)^{x} . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places.
 The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is  g(x)=\ldots(\ldots)^{x} . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places.  <div style=padding-top: 35px>
Question
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   Which one is exponential:  f, g , or  h  ?<div style=padding-top: 35px>
Which one is exponential: f,gf, g , or hh ?
Question
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)   <div style=padding-top: 35px>
The following three graphs correspond with the functions in the table. Which is the graph of gg ?

A)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)   <div style=padding-top: 35px>
B)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)   <div style=padding-top: 35px>
C)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)   <div style=padding-top: 35px>
Question
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The formula for the exponential one is  \ldots(\ldots)^{t} Round your second answer to 2 decimal places.<div style=padding-top: 35px>
The formula for the exponential one is ()t\ldots(\ldots)^{t} Round your second answer to 2 decimal places.
Question
The population of a city is increasing exponentially. In 2000 , the city had a population of 40,000 . In 2005 , the population was 58,502. The formula for P(t)P(t) , the population of the town tt years after 2000 , is given by p(t)=()tp(t)=\ldots(\ldots)^{t} .Round your second answer to 3 decimal places.
Question
The formula for the exponential function PP such that P(11)=10P(11)=10 and P(12)=9P(12)=9 is given by P(t)=()tP(t)=\ldots(\ldots)^{t} . Give both answers to 3 decimal places.
Question
Find a possible formula for the exponential function ff such that the points (5,2684.355)(5,2684.355) and (3,262.144)(3,262.144) are on the graph.
Question
Write the formula for the price pp of a gallon of gas in tt days if the price is $3.85\$ 3.85 on day tt =0=0 and the price increases by $0.08\$ 0.08 per day.
Question
Write the formula for the price pp of a gallon of gas in tt days if the price is $3.35\$ 3.35 on day tt =0=0 and the price increases by 7%7 \% per day.
Question
One solution to the equation 3+x=3(2)x3+x=3(2)^{x} is x=0x=0 . Use your calculator to estimate the other solution to 2 decimal places.
Question
What is the maximum number of solutions the equation 2+x=2(4)x2+x=2(4)^{x} can have?
Question
The graph of the exponential function P(t)P(t) is shown below. The formula for p(t)=()tp(t)=\ldots(\ldots)^{t}
 The graph of the exponential function  P(t)  is shown below. The formula for  p(t)=\ldots(\ldots)^{t}   <div style=padding-top: 35px>
Question
The graph of the exponential function P(t)P(t) is shown below. Suppose P(t)P(t) represents a city's population, in thousands, tt years after 1995. Which of the following quantities are equivalent?
 <strong>The graph of the exponential function  P(t)  is shown below. Suppose  P(t)  represents a city's population, in thousands,  t  years after 1995. Which of the following quantities are equivalent?   </strong> A)   P(7)-P(4)  B) Approximately -125 thousand C) Approximately 387 thousand D) The change in the city's population between 1999 and 2002 E)   P(7)/P(4)  F) The rate at which the population is declining between 1999 and 2002 <div style=padding-top: 35px>

A) P(7)P(4) P(7)-P(4)
B) Approximately -125 thousand
C) Approximately 387 thousand
D) The change in the city's population between 1999 and 2002
E) P(7)/P(4) P(7)/P(4)
F) The rate at which the population is declining between 1999 and 2002
Question
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%1.34 \% per year. Some demographers believe that the ideal population of the United States is about 130 million. According to this model, in what year did this occur?
Question
Find limt20,000(0.82)t\lim _{t \rightarrow \infty} 20,000(0.82)^{t} . For \infty or -\infty , enter "inf" or "-inf".
Question
Find limx7.2e0.11x\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x} . For \infty or -\infty , enter "inf" or "-inf".
Question
In the following figure, the functions f,g,hf, g, h , and pp can all be written in the form y=abty=a b^{t} . Which one has the largest value for bb ?
 In the following figure, the functions  f, g, h , and  p  can all be written in the form  y=a b^{t} . Which one has the largest value for  b  ?  <div style=padding-top: 35px>
Question
Solve y=18(0.84)xy=18(0.84)^{x} graphically for xx if y=13y=13 . Round to 2 decimal places.
Question
The price of an item increases due to inflation. Let p(t)=12.50(1.024)tp(t)=12.50(1.024)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004 . Estimate p1(75)p^{-1}(75) to 2 decimal places.
Question
Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of 0.27%0.27 \% per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.
Question
The population of a city is increasing exponentially. In 2000 , the city had a population of 70,000. In 2003, the population was 89,870 . Let P(t)P(t) be the population of the town tt years after 2000 . Use a graph of P(t)P(t) to estimate the year in which the population will reach 250,000 .
Question
The following figure gives the graph of C=f(t)C=f(t) , where C\mathrm{C} is the computer hard disk capacity (in hundreds of megabytes) that could be bought for $500t\$ 500 t years past 1989 . If the trend displayed in the graph continued, how many megabytes would a $500\$ 500 hard drive have in 1997? Round to the nearest hundred.
CC , capacity (in 100 s of megabytes)
 The following figure gives the graph of  C=f(t) , where  \mathrm{C}  is the computer hard disk capacity (in hundreds of megabytes) that could be bought for  \$ 500 t  years past 1989 . If the trend displayed in the graph continued, how many megabytes would a  \$ 500  hard drive have in 1997? Round to the nearest hundred.  C , capacity (in 100 s of megabytes)  <div style=padding-top: 35px>
Question
The following figure gives the graph of C=f(t)C=f(t) , where C\mathrm{C} is the computer hard disk capacity (in hundreds of megabytes) that could be bought for $500t\$ 500 t years past 1989 . If the trend displayed in the graph continued, in what year would the capacity that can be bought for $500\$ 500 be 4,600 ?
C, capacity (in 100 s of megabytes) C \text {, capacity (in } 100 \text { s of megabytes) }
 The following figure gives the graph of  C=f(t) , where  \mathrm{C}  is the computer hard disk capacity (in hundreds of megabytes) that could be bought for  \$ 500 t  years past 1989 . If the trend displayed in the graph continued, in what year would the capacity that can be bought for  \$ 500  be 4,600 ?  C \text {, capacity (in } 100 \text { s of megabytes) }   <div style=padding-top: 35px>
Question
Which of the following characteristics describe the graph of f(x)=(1.5)xf(x)=(1.5)^{x} ?

A) It is concave down.
B) It is concave up.
C) It crosses the yy -axis at 1 .
D) As x,f(x)x \rightarrow \infty, f(x) \rightarrow \infty .
E) As x,f(x)0x \rightarrow \infty, f(x) \rightarrow 0 .
F) As x,f(x)x \rightarrow-\infty, f(x) \rightarrow \infty .
G) As x,f(x)0x \rightarrow-\infty, f(x) \rightarrow 0 .
Question
The amount of pollution in a harbor tt hours after it was contaminated by illegal dumping is given by A=50(0.8)tA=50(0.8)^{t} tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.
Question
What is the horizontal asymptote of y=87(0.64)ty=87(0.64)^{t} as tt \rightarrow \infty ?

A) y=0.64y=0.64
B) y=87y=87
C) y=0y=0
D) There isn't one
Question
Consider the following figure, where Graph I has equation y=a1eb1xy=a_{1} e^{b_{1} x} , Graph II has equation y=a2eb2xy=a_{2} e^{b_{2} x} , Graph III has equation y=a3eb3xy=a_{3} e^{b_{3} x} , and Graph IV has equation y=a4eb4xy=a_{4} e^{b_{4} x} .
 Consider the following figure, where Graph I has equation  y=a_{1} e^{b_{1} x} , Graph II has equation  y=a_{2} e^{b_{2} x} , Graph III has equation  y=a_{3} e^{b_{3} x} , and Graph IV has equation  y=a_{4} e^{b_{4} x} .   Is  b_{1}  positive or negative?<div style=padding-top: 35px>
Is b1b_{1} positive or negative?
Question
Let (x0,y0)\left(x_{0}, y_{0}\right) be the intersection of the graphs of the two exponential functions y=aebxy=a e^{b x} and y=cedxy=c e^{d x} , where 0<a<c0<a<c . If aa is increased, does x0x_{0} increase, decrease, or stay the same?
Question
Let (t0,P(t0))\left(t_{0}, P\left(t_{0}\right)\right) be the intersection of the graphs of the two exponential functions P=a(1+r)tP=a(1+r)^{t} and P=b(1+s)tP=b(1+s)^{t} , where 0<a<b0<a<b . If rr is increased, does P(t0)P\left(t_{0}\right) increase, decrease, or stay the same?
Question
Assume that all important features are shown in the following graph of y=f(x)y=f(x) .
What is limxf(x)\lim _{x \rightarrow-\infty} f(x) ? For \infty or -\infty , enter "inf" or "-inf".
 Assume that all important features are shown in the following graph of  y=f(x) . What is  \lim _{x \rightarrow-\infty} f(x)  ? For  \infty  or  -\infty , enter inf or -inf.  <div style=padding-top: 35px>
Question
The graph of P(t)=1.7t+29P(t)=1.7^{-t}+29 has a horizontal asymptote at P(t)=P(t)= ---------. (If there is no horizontal asymptote, enter "DNE".)
Question
Is the function graphed exponential?
Is the function graphed exponential?  <div style=padding-top: 35px>
Question
Is the function graphed exponential?
Is the function graphed exponential?  <div style=padding-top: 35px>
Question
Solve y=5(1.1)xy=5(1.1)^{x} for xx if y=6.655y=6.655 .
Question
An investment grows according to the formula V=7000e0.051tV=7000 e^{0.051 t} . How many years will it take for the original investment to triple? Round to 1 decimal place.
Question
The price of an item increases due to inflation. Let p(t)=32.50(1.047)tp(t)=32.50(1.047)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.
Question
Is the formula for a function representing a quantity which begins at NN in year t=0t=0 and grows at a constant annual rate of r%r \% given by
f(t)=r(1+N)t?f(t)=r(1+N)^{t} ?
Question
Is the formula for a function representing a quantity which begins at 4N4 N in year t=0t=0 and grows at a continuous annual rate of r%r \% given by
f(t)=4Nert/100?f(t)=4 N e^{r t /100} ?
Question
Is the formula for a function representing a quantity which begins at an amount 35%35 \% larger than NN in year t=0t=0 and grows at a continuous annual rate of r%r \% given by f(t)=1.35Nert/100f(t)=1.35 N e^{r t /100} ?
Question
Is the formula for a function representing a quantity which begins at NN in year t=0t=0 and grows at a continuous annual rate of r3%\frac{r}{3} \% given by
f(t)=Nert3?f(t)=N e^{\frac{r t}{3}} ?
Question
Let P(t)=4,500e0.043tP(t)=4,500 e^{0.043 t} give the size of a population of animals in year tt . What will the population be after 12 years? Round to the nearest whole number.
Question
Let P(t)=5,000e0.037tP(t)=5,000 e^{0.037 t} give the size of a population of animals in year tt . After how many years will the population be approximately 10,099 ? Round to the nearest year.
Question
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%1.34 \% per year. What is the formula for P(t)P(t) , the population for the United States tt years after 2005?

A) P(t)=296.4(0.0134)tP(t)=296.4(0.0134)^{t}
B) P(t)=296.4(1.0134)t P(t)=296.4(1.0134)^{t}
C) P(t)=296.4e1.0134t P(t)=296.4 e^{1.0134 t}
D) P(t)=296.4e0.0134t P(t)=296.4 e^{0.0134 t}
Question
The figure below shows the graphs of the following functions:
(A) y=ety=e^{t}
(B) y=2ty=2^{t}
(C) y=ety=e^{-t}
(D) y=2ty=2^{-t}
 The figure below shows the graphs of the following functions: (A)  y=e^{t}  (B)  y=2^{t}  (C)  y=e^{-t}  (D)  y=2^{-t}    Which one is the graph of A?<div style=padding-top: 35px>
Which one is the graph of A?
Question
What is limxe4x\lim _{x \rightarrow \infty} e^{-4 x} ? If necessary, enter "inf" for \infty and "-inf" for -\infty .
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Deck 4: Exponential Functions
1
In the exponential formula Q=47,200(0.9)tQ=47,200(0.9)^{t} , if Q=a(1+r)tQ=a(1+r)^{t} then r=%r=\ldots \% .
-10
2
In 2006, the cost of a particular piece of computer equipment was $490\$ 490 and going down at a rate of 14%14 \% per year. Assuming this percentage remains constant, what is the formula for CC , the cost of this equipment in dollars, as a function of tt , the number of years since 2006 ?

A) C=490(0.86)t C=490(0.86)^{t}
B) C=490(1.14)t C=490(-1.14)^{t}
C) C=490(0.14)t C=490(0.14)^{t}
D) C=490(0.86)t C=490(-0.86)^{t}
C=490(0.86)t C=490(0.86)^{t}
3
If you start with $8,000\$ 8,000 , how much money will you have after a 10%10 \% increase?
$8,800\$ 8,800
4
If you start with $6,000\$ 6,000 , how much money will you have after a 5%5 \% increase followed by a 25%25 \% decrease?
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5
Which of the graphs in the following figure is the graph of 150(1.1)t150(1.1)^{t} ?
 Which of the graphs in the following figure is the graph of  150(1.1)^{t}  ?
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6
What is the growth factor if sales increase by 37%37 \% each month?
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7
The populations of 4 species of animals are given by the following equations:
P1=650(0.71)tP2=600(1.2)tP3=270(0.88)tP4=610(1.05)tP_{1}=650(0.71)^{t} P_{2}=600(1.2)^{t} P_{3}=270(0.88)^{t} P_{4}=610(1.05)^{t}
Which species are shrinking in size?

A) P4P_{4}
B) P3P_{3}
C) P2P_{2}
D) P1P_{1}
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8
The populations of 4 species of animals are given by the following equations:
P1=470(0.81)tP2=900(1.28)tP3=670(0.73)tP4=640(1.05)tP_{1}=470(0.81)^{t} P_{2}=900(1.28)^{t} P_{3}=670(0.73)^{t} P_{4}=640(1.05)^{t}
What is the annual percent growth rate for the population that is growing the fastest?
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9
The populations of 4 species of animals are given by the following equations:
P1=390(0.75)tP2=100(1.09)tP3=230(0.82)tP4=600(1.05)tP_{1}=390(0.75)^{t} P_{2}=100(1.09)^{t} P_{3}=230(0.82)^{t} P_{4}=600(1.05)^{t}
What is the largest initial population of the 4 species?
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10
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.38%1.38 \% per year. How many million people would you expect to live in the United States in the year 2020? Round to 1 decimal place.
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11
A quantity decreased from 100 to 95 . By what percentage did it decrease?
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12
A store's sales of cassette tapes of music decreased by 6%6 \% per year over a period of 5 years. By what total percent did sales of cassette tapes decrease over this time period? Round to 1 decimal place.
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13
The population of a city has been growing at a rate of 4%4 \% per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.
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14
In some developing countries, the inflation rate has been as high as 0.94%0.94 \% per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.
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15
The price of an item increases due to inflation. Let p(t)=22.50(1.037)tp(t)=22.50(1.037)^{t} be the price of the item as a function of time in years, with t=0t=0 in 2004. What is the weekly inflation rate? Round to 2 decimal places.
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16
The price of an item increases due to inflation. Let p(t)=22.50(1.029)tp(t)=22.50(1.029)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004. What is the practical interpretation of p1(70)p^{-1}(70) ?

A) The price in 2004 of an item that is $70\$ 70 now.
B) The price now of an item that was $70 in 2004.
C) The time at which the price reaches $70\$ 70 .
D) The price of the item after 70 years.
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17
The amount of pollution in a harbor tt hours after it was contaminated by illegal dumping is given by A=70(0.65)tA=70(0.65)^{t} tons. What percentage of the pollution leaves the harbor each hour?
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18
A radioactive substance decays by 12%12 \% every year. Which of the following is the formula for the quantity, QQ , of a 10 gram sample remaining after tt years?

A) Q=10(0.88)tQ=10(0.88)^{t}
B) Q=10(1.12)tQ=10(1.12)^{t}
C) Q=10(1.12)tQ=10(-1.12)^{t}
D) Q=10(0.88)tQ=10(-0.88)^{t}
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19
Which equation has a rate of change of 9%9 \% ?

A) Q=(3,200)0.91tQ=(3,200) 0.91^{t}
B) Q=(3,200)109tQ=(3,200) 109^{t}
C) Q=(3,200)1.09t Q=(3,200) 1.09^{t}
D) Q=(3,200)91tQ=(3,200) 91^{t}
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20
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-1(0.8)^{x}  B)  y=1(0.8)^{x}  C)  y=1(1.2)^{-x}  D)  y=1(1.2)^{x}

A) y=1(0.8)xy=-1(0.8)^{x}
B) y=1(0.8)xy=1(0.8)^{x}
C) y=1(1.2)xy=1(1.2)^{-x}
D) y=1(1.2)xy=1(1.2)^{x}
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21
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-4(1.1)^{x}  B)  y=4(1.1)^{x}  C)  y=4(0.9)^{-x}  D)  y=4(0.9)^{x}

A) y=4(1.1)xy=-4(1.1)^{x}
B) y=4(1.1)xy=4(1.1)^{x}
C) y=4(0.9)xy=4(0.9)^{-x}
D) y=4(0.9)xy=4(0.9)^{x}
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22
Match the graph to its equation.
 <strong>Match the graph to its equation.   </strong> A)  y=-4(1.1)^{x}  B)  y=4(1.1)^{x}  C)  y=4(0.9)^{-x}  D)  y=4(0.9)^{x}

A) y=4(1.1)xy=-4(1.1)^{x}
B) y=4(1.1)xy=4(1.1)^{x}
C) y=4(0.9)xy=4(0.9)^{-x}
D) y=4(0.9)xy=4(0.9)^{x}
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23
Which of the following formulas are exponential?

A) P(t)=8.9(1.21)t P(t)=8.9(1.21)^{t}
B) P(t)=1.899.68t P(t)=1.89-9.68 t
C) P(t)=17.8t+40.05t22.25 P(t)=17.8^{t}+40.05 t-22.25
D) P(t)=(1.4641)t2670 P(t)=(1.4641)^{t} 2670
E) P(t)=178e2.42t P(t)=178 e^{2.42 t}
F) P(t)=1.78e0.605t P(t)=1.78 e^{-0.605 t}
G) P(t)=(4.45+12.1t)t P(t)=(4.45+12.1 t)^{t}
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24
The average life expectancy in a country tends to increase by the same percentage each year. Should a linear or an exponential function be used to model this scenario?
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25
The following table gives values from an exponential or a linear function. Determine which, and find values for aa and bb so that f(x)=a+bxf(x)=a+b x if the function is linear, or f(x)=a(b)xf(x)=a(b)^{x} if the function is exponential.
a= ---------------,b= ------------
 The following table gives values from an exponential or a linear function. Determine which, and find values for  a  and  b  so that  f(x)=a+b x  if the function is linear, or  f(x)=a(b)^{x}  if the function is exponential. a= ---------------,b= ------------
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26
The table below shows vv , the dollar value of a share of a certain stock, as a function of tt , the time (in weeks) since the initial offering of the stock. A possible formula for v(t)v(t) is v(t)=()tv(t)=\ldots(\ldots)^{t} . Round the second answer to 3 decimal places.
 The table below shows  v , the dollar value of a share of a certain stock, as a function of  t , the time (in weeks) since the initial offering of the stock. A possible formula for  v(t)  is  v(t)=\ldots(\ldots)^{t} . Round the second answer to 3 decimal places.
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27
A population has size 3,500 at time t=0t=0 , with tt in years. If the population grows by 80 people per year, what is the formula for PP , the population at time tt ?

A) P=3,500(1.8)t P=3,500(1.8) t
B) P=3,500+80t P=3,500+80 t
C) P=3,500(0.8)t P=3,500(0.8)^{t}
D) P=3,500(1.8)t P=3,500(1.8)^{t}
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28
A population has size 3,000 at time t=0t=0 , with tt in years. If the population grows by 10%10 \% per year, what is the formula for PP , the population at time tt ?

A) P=3,000(1.1)t P=3,000(1.1) t
B) P=3,000+10t P=3,000+10 t
C) P=3,000(1.1)t P=3,000(1.1)^{t}
D) P=3,000(0.1)t P=3,000(0.1)^{t}
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29
The graph below shows the quantity of a drug in a patient's bloodstream over a period of time tt , in minutes.
 <strong>The graph below shows the quantity of a drug in a patient's bloodstream over a period of time  t , in minutes.   Which of the following scenarios best describes the graph?</strong> A) The drug is injected over a 10 minute interval, during which the quantity increases linearly. After the 10 minutes, the injection is discontinued and the quantity then decays exponentially. B) The drug is injected over a 10 minute interval, during which the quantity increases exponentially. After the 10 minutes, the injection is discontinued and the quantity then decays linearly. C) The drug is injected all at once. The quantity first increases and then decreases linearly. D) The drug is injected all at once. The quantity first increases and then decreases exponentially.
Which of the following scenarios best describes the graph?

A) The drug is injected over a 10 minute interval, during which the quantity increases linearly. After the 10 minutes, the injection is discontinued and the quantity then decays exponentially.
B) The drug is injected over a 10 minute interval, during which the quantity increases exponentially. After the 10 minutes, the injection is discontinued and the quantity then decays linearly.
C) The drug is injected all at once. The quantity first increases and then decreases linearly.
D) The drug is injected all at once. The quantity first increases and then decreases exponentially.
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30
Kevin buys a new CD player for $300\$ 300 , and finds two years later when he wants to sell it that it is only worth $82\$ 82 . Assuming the value of the CD player decreases exponentially, the formula for V(t)V(t) , the value of the CD player after tt years, is given by V(t)=()tV(t)=\ldots(\ldots)^{t} . Round your second answer to 2 decimal places.
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31
A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 15 hours after the spill. She sets up a possible model to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 6 tons\hour. She estimates that the lake will be free from the contaminant 35 hours after the spill. How many tons of the contaminant were in the lake at the 15 hour reading?
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32
A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 3 tons\hour. Using this model, she estimates that the lake will be free from the contaminant 20 hours after the spill. Thus, Q(2)= ---------- and Q(11)= ----------- The second model assumes that the amount of contaminant decreases exponentially. In this model, she finds that Q(t)=()tQ(t)=\ldots(\ldots)^{t} . Round both answers to 3 decimal places.
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33
A biologist measures the amount of contaminant in a lake 3 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine QQ , the amount of the chemical remaining in the lake as a function of tt , the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 7 tons\hour. Using this model, she estimates that the lake will be free from the contaminant 24 hours after the spill. The second model assumes that the amount of contaminant decreases exponentially. She measures the spill a third time after 23 hours and finds that 44 tons remain. Which model seems best?

A) The linear one
B) The exponential one
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34
Let f(x)f(x) be given in the table below. Find the value of kk if f(x)f(x) is linear.
 Let  f(x)  be given in the table below. Find the value of  k  if  f(x)  is linear.
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35
Let f(x)f(x) be given in the table below. Find the value of kk if f(x)f(x) is exponential.
 Let  f(x)  be given in the table below. Find the value of  k  if  f(x)  is exponential.
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36
The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is g(x)=()xg(x)=\ldots(\ldots)^{x} . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places.
 The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is  g(x)=\ldots(\ldots)^{x} . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places.
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37
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   Which one is exponential:  f, g , or  h  ?
Which one is exponential: f,gf, g , or hh ?
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38
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)
The following three graphs correspond with the functions in the table. Which is the graph of gg ?

A)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)
B)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)
C)
 <strong>Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The following three graphs correspond with the functions in the table. Which is the graph of  g  ?</strong> A)   B)   C)
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39
Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.
 Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither.   The formula for the exponential one is  \ldots(\ldots)^{t} Round your second answer to 2 decimal places.
The formula for the exponential one is ()t\ldots(\ldots)^{t} Round your second answer to 2 decimal places.
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40
The population of a city is increasing exponentially. In 2000 , the city had a population of 40,000 . In 2005 , the population was 58,502. The formula for P(t)P(t) , the population of the town tt years after 2000 , is given by p(t)=()tp(t)=\ldots(\ldots)^{t} .Round your second answer to 3 decimal places.
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41
The formula for the exponential function PP such that P(11)=10P(11)=10 and P(12)=9P(12)=9 is given by P(t)=()tP(t)=\ldots(\ldots)^{t} . Give both answers to 3 decimal places.
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42
Find a possible formula for the exponential function ff such that the points (5,2684.355)(5,2684.355) and (3,262.144)(3,262.144) are on the graph.
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43
Write the formula for the price pp of a gallon of gas in tt days if the price is $3.85\$ 3.85 on day tt =0=0 and the price increases by $0.08\$ 0.08 per day.
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44
Write the formula for the price pp of a gallon of gas in tt days if the price is $3.35\$ 3.35 on day tt =0=0 and the price increases by 7%7 \% per day.
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45
One solution to the equation 3+x=3(2)x3+x=3(2)^{x} is x=0x=0 . Use your calculator to estimate the other solution to 2 decimal places.
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46
What is the maximum number of solutions the equation 2+x=2(4)x2+x=2(4)^{x} can have?
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47
The graph of the exponential function P(t)P(t) is shown below. The formula for p(t)=()tp(t)=\ldots(\ldots)^{t}
 The graph of the exponential function  P(t)  is shown below. The formula for  p(t)=\ldots(\ldots)^{t}
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48
The graph of the exponential function P(t)P(t) is shown below. Suppose P(t)P(t) represents a city's population, in thousands, tt years after 1995. Which of the following quantities are equivalent?
 <strong>The graph of the exponential function  P(t)  is shown below. Suppose  P(t)  represents a city's population, in thousands,  t  years after 1995. Which of the following quantities are equivalent?   </strong> A)   P(7)-P(4)  B) Approximately -125 thousand C) Approximately 387 thousand D) The change in the city's population between 1999 and 2002 E)   P(7)/P(4)  F) The rate at which the population is declining between 1999 and 2002

A) P(7)P(4) P(7)-P(4)
B) Approximately -125 thousand
C) Approximately 387 thousand
D) The change in the city's population between 1999 and 2002
E) P(7)/P(4) P(7)/P(4)
F) The rate at which the population is declining between 1999 and 2002
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49
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%1.34 \% per year. Some demographers believe that the ideal population of the United States is about 130 million. According to this model, in what year did this occur?
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50
Find limt20,000(0.82)t\lim _{t \rightarrow \infty} 20,000(0.82)^{t} . For \infty or -\infty , enter "inf" or "-inf".
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51
Find limx7.2e0.11x\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x} . For \infty or -\infty , enter "inf" or "-inf".
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52
In the following figure, the functions f,g,hf, g, h , and pp can all be written in the form y=abty=a b^{t} . Which one has the largest value for bb ?
 In the following figure, the functions  f, g, h , and  p  can all be written in the form  y=a b^{t} . Which one has the largest value for  b  ?
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53
Solve y=18(0.84)xy=18(0.84)^{x} graphically for xx if y=13y=13 . Round to 2 decimal places.
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54
The price of an item increases due to inflation. Let p(t)=12.50(1.024)tp(t)=12.50(1.024)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004 . Estimate p1(75)p^{-1}(75) to 2 decimal places.
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55
Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of 0.27%0.27 \% per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.
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56
The population of a city is increasing exponentially. In 2000 , the city had a population of 70,000. In 2003, the population was 89,870 . Let P(t)P(t) be the population of the town tt years after 2000 . Use a graph of P(t)P(t) to estimate the year in which the population will reach 250,000 .
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57
The following figure gives the graph of C=f(t)C=f(t) , where C\mathrm{C} is the computer hard disk capacity (in hundreds of megabytes) that could be bought for $500t\$ 500 t years past 1989 . If the trend displayed in the graph continued, how many megabytes would a $500\$ 500 hard drive have in 1997? Round to the nearest hundred.
CC , capacity (in 100 s of megabytes)
 The following figure gives the graph of  C=f(t) , where  \mathrm{C}  is the computer hard disk capacity (in hundreds of megabytes) that could be bought for  \$ 500 t  years past 1989 . If the trend displayed in the graph continued, how many megabytes would a  \$ 500  hard drive have in 1997? Round to the nearest hundred.  C , capacity (in 100 s of megabytes)
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58
The following figure gives the graph of C=f(t)C=f(t) , where C\mathrm{C} is the computer hard disk capacity (in hundreds of megabytes) that could be bought for $500t\$ 500 t years past 1989 . If the trend displayed in the graph continued, in what year would the capacity that can be bought for $500\$ 500 be 4,600 ?
C, capacity (in 100 s of megabytes) C \text {, capacity (in } 100 \text { s of megabytes) }
 The following figure gives the graph of  C=f(t) , where  \mathrm{C}  is the computer hard disk capacity (in hundreds of megabytes) that could be bought for  \$ 500 t  years past 1989 . If the trend displayed in the graph continued, in what year would the capacity that can be bought for  \$ 500  be 4,600 ?  C \text {, capacity (in } 100 \text { s of megabytes) }
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59
Which of the following characteristics describe the graph of f(x)=(1.5)xf(x)=(1.5)^{x} ?

A) It is concave down.
B) It is concave up.
C) It crosses the yy -axis at 1 .
D) As x,f(x)x \rightarrow \infty, f(x) \rightarrow \infty .
E) As x,f(x)0x \rightarrow \infty, f(x) \rightarrow 0 .
F) As x,f(x)x \rightarrow-\infty, f(x) \rightarrow \infty .
G) As x,f(x)0x \rightarrow-\infty, f(x) \rightarrow 0 .
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60
The amount of pollution in a harbor tt hours after it was contaminated by illegal dumping is given by A=50(0.8)tA=50(0.8)^{t} tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.
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61
What is the horizontal asymptote of y=87(0.64)ty=87(0.64)^{t} as tt \rightarrow \infty ?

A) y=0.64y=0.64
B) y=87y=87
C) y=0y=0
D) There isn't one
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62
Consider the following figure, where Graph I has equation y=a1eb1xy=a_{1} e^{b_{1} x} , Graph II has equation y=a2eb2xy=a_{2} e^{b_{2} x} , Graph III has equation y=a3eb3xy=a_{3} e^{b_{3} x} , and Graph IV has equation y=a4eb4xy=a_{4} e^{b_{4} x} .
 Consider the following figure, where Graph I has equation  y=a_{1} e^{b_{1} x} , Graph II has equation  y=a_{2} e^{b_{2} x} , Graph III has equation  y=a_{3} e^{b_{3} x} , and Graph IV has equation  y=a_{4} e^{b_{4} x} .   Is  b_{1}  positive or negative?
Is b1b_{1} positive or negative?
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63
Let (x0,y0)\left(x_{0}, y_{0}\right) be the intersection of the graphs of the two exponential functions y=aebxy=a e^{b x} and y=cedxy=c e^{d x} , where 0<a<c0<a<c . If aa is increased, does x0x_{0} increase, decrease, or stay the same?
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64
Let (t0,P(t0))\left(t_{0}, P\left(t_{0}\right)\right) be the intersection of the graphs of the two exponential functions P=a(1+r)tP=a(1+r)^{t} and P=b(1+s)tP=b(1+s)^{t} , where 0<a<b0<a<b . If rr is increased, does P(t0)P\left(t_{0}\right) increase, decrease, or stay the same?
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65
Assume that all important features are shown in the following graph of y=f(x)y=f(x) .
What is limxf(x)\lim _{x \rightarrow-\infty} f(x) ? For \infty or -\infty , enter "inf" or "-inf".
 Assume that all important features are shown in the following graph of  y=f(x) . What is  \lim _{x \rightarrow-\infty} f(x)  ? For  \infty  or  -\infty , enter inf or -inf.
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66
The graph of P(t)=1.7t+29P(t)=1.7^{-t}+29 has a horizontal asymptote at P(t)=P(t)= ---------. (If there is no horizontal asymptote, enter "DNE".)
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67
Is the function graphed exponential?
Is the function graphed exponential?
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68
Is the function graphed exponential?
Is the function graphed exponential?
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69
Solve y=5(1.1)xy=5(1.1)^{x} for xx if y=6.655y=6.655 .
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70
An investment grows according to the formula V=7000e0.051tV=7000 e^{0.051 t} . How many years will it take for the original investment to triple? Round to 1 decimal place.
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71
The price of an item increases due to inflation. Let p(t)=32.50(1.047)tp(t)=32.50(1.047)^{t} give the price of the item as a function of time in years, with t=0t=0 in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.
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72
Is the formula for a function representing a quantity which begins at NN in year t=0t=0 and grows at a constant annual rate of r%r \% given by
f(t)=r(1+N)t?f(t)=r(1+N)^{t} ?
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73
Is the formula for a function representing a quantity which begins at 4N4 N in year t=0t=0 and grows at a continuous annual rate of r%r \% given by
f(t)=4Nert/100?f(t)=4 N e^{r t /100} ?
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74
Is the formula for a function representing a quantity which begins at an amount 35%35 \% larger than NN in year t=0t=0 and grows at a continuous annual rate of r%r \% given by f(t)=1.35Nert/100f(t)=1.35 N e^{r t /100} ?
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75
Is the formula for a function representing a quantity which begins at NN in year t=0t=0 and grows at a continuous annual rate of r3%\frac{r}{3} \% given by
f(t)=Nert3?f(t)=N e^{\frac{r t}{3}} ?
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76
Let P(t)=4,500e0.043tP(t)=4,500 e^{0.043 t} give the size of a population of animals in year tt . What will the population be after 12 years? Round to the nearest whole number.
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77
Let P(t)=5,000e0.037tP(t)=5,000 e^{0.037 t} give the size of a population of animals in year tt . After how many years will the population be approximately 10,099 ? Round to the nearest year.
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78
The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%1.34 \% per year. What is the formula for P(t)P(t) , the population for the United States tt years after 2005?

A) P(t)=296.4(0.0134)tP(t)=296.4(0.0134)^{t}
B) P(t)=296.4(1.0134)t P(t)=296.4(1.0134)^{t}
C) P(t)=296.4e1.0134t P(t)=296.4 e^{1.0134 t}
D) P(t)=296.4e0.0134t P(t)=296.4 e^{0.0134 t}
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79
The figure below shows the graphs of the following functions:
(A) y=ety=e^{t}
(B) y=2ty=2^{t}
(C) y=ety=e^{-t}
(D) y=2ty=2^{-t}
 The figure below shows the graphs of the following functions: (A)  y=e^{t}  (B)  y=2^{t}  (C)  y=e^{-t}  (D)  y=2^{-t}    Which one is the graph of A?
Which one is the graph of A?
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80
What is limxe4x\lim _{x \rightarrow \infty} e^{-4 x} ? If necessary, enter "inf" for \infty and "-inf" for -\infty .
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