Question 1

What is $\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$.

Accepted Answer

The answer of What is $\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)$...

Question 2

A population has size 3,500 at time $t=0$, with $t$ in years. If the population grows by 80 people per year, what is the formula for $P$, the population at time $t$ ?

Accepted Answer

A)  $ P=3,500(1.8) t$ 
B)  $ P=3,500+80 t$ 
C)  $ P=3,500(0.8)^{t}$ 
D)  $ P=3,500(1.8)^{t}$

Question 3

$\lim _{x \rightarrow \infty} 6 e^{3 x}=0$

Accepted Answer

A) True 
 B)False

Question 4

Let $P(t)=5,000 e^{0.037 t}$ give the size of a population of animals in year $t$. After how many years will the population be approximately 10,099 ? Round to the nearest year.

Accepted Answer

The answer of Let $P(t)=5,000 e^{0.037 t}$ give the size...

Question 5

Match the graph to its equation.

Accepted Answer

A)  $y=-4(1.1)^{x}$ 
B)  $y=4(1.1)^{x}$ 
C)  $y=4(0.9)^{-x}$ 
D)  $y=4(0.9)^{x}$

Question 6

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a constant annual rate of $r \%$ given by
$f(t)=r(1+N)^{t} ?$

Accepted Answer

A) True 
 B)False

Question 7

What is the growth factor if sales increase by $37 \%$ each month?

Accepted Answer

The answer of What is the growth factor if sales...

Question 8

Find a possible formula for the exponential function $f$ such that the points $(5,2684.355)$ and $(3,262.144)$ are on the graph.

Accepted Answer

The answer of Find a possible formula for the exponential...

Question 9

Jeff has $\$ 40,000$. He placed $\$ 20,000$ in Bank 1 with an account earning $3.4 \%$ annual interest, compounded continuously. He also placed \$20,000 in Bank 2 with an account earning 3.6\% annual interest compounded weekly. After 10 years,
A) how much money is in Bank 1 ?
B) how much money is in Bank 2?

Accepted Answer

The answer of Jeff has $\$ 40,000$. He placed \(\$...

Question 10

Which of the graphs in the following figure is the graph of $150(1.1)^{t}$ ?

Accepted Answer

The answer of Which of the graphs in the following...

Question 11

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=50(0.8)^{t}$ tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.

Accepted Answer

The answer of The amount of pollution in a harbor...

Question 12

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 $Q$, the amount of the chemical remaining in the lake as a function of $t$, 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?

Accepted Answer

A)  The linear one 
B)  The exponential one

Question 13

Is the function graphed exponential?

Accepted Answer

A) True 
 B)False

Question 14

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 ?
$C \text {, capacity (in } 100 \text { s of megabytes) }$

Accepted Answer

The answer of The following figure gives the graph of...

Question 15

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.

Accepted Answer

The answer of Each of the functions in the table...

Question 16

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ 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?

Accepted Answer

The answer of The US population in 2005 was approximately...

Question 17

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 $Q$, the amount of the chemical remaining in the lake as a function of $t$, 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?

Accepted Answer

The answer of A biologist measures the amount of contaminant...

Question 18

What is $\lim _{x \rightarrow \infty} e^{-4 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$.

Accepted Answer

The answer of What is \(\lim _{x \rightarrow \infty} e^{-4...

Question 19

An ant population grows at a continuous growth rate of $11.3 \%$. If the population starts with 22,000 ants, how many ants are there after 6 months? Round your answer to the nearest ant.

Accepted Answer

The answer of An ant population grows at a continuous...

Question 20

The price of an item increases due to inflation. Let $p(t)=22.50(1.029)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. What is the practical interpretation of $p^{-1}(70)$ ?

Accepted Answer

A)  The price in 2004 of an item that is $\$ 70$ now. 
B)  The price now of an item that was $70 in 2004. 
C)  The time at which the price reaches $\$ 70$. 
D)  The price of the item after 70 years.

Exam 4: Exponential Functions

What is $\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

A population has size 3,500 at time $t=0$ , with $t$ in years. If the population grows by 80 people per year, what is the formula for $P$ , the population at time $t$ ?

$\lim _{x \rightarrow \infty} 6 e^{3 x}=0$

Let $P(t)=5,000 e^{0.037 t}$ give the size of a population of animals in year $t$ . After how many years will the population be approximately 10,099 ? Round to the nearest year.

Match the graph to its equation. $Match the graph to its equation. A) y=-4(1.1) ^{x} B) y=4(1.1) ^{x} C) y=4(0.9) ^{-x} D) y=4(0.9) ^{x}$

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a constant annual rate of $r \%$ given by $f(t)=r(1+N)^{t} ?$

What is the growth factor if sales increase by $37 \%$ each month?

Find a possible formula for the exponential function $f$ such that the points $(5,2684.355)$ and $(3,262.144)$ are on the graph.

Which of the graphs in the following figure is the graph of $150(1.1)^{t}$ ? $Which of the graphs in the following figure is the graph of 150(1.1)^{t} ?$

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=50(0.8)^{t}$ tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.

Is the function graphed exponential?

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ 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?

What is $\lim _{x \rightarrow \infty} e^{-4 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

An ant population grows at a continuous growth rate of $11.3 \%$ . If the population starts with 22,000 ants, how many ants are there after 6 months? Round your answer to the nearest ant.

The price of an item increases due to inflation. Let $p(t) =22.50(1.029) ^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. What is the practical interpretation of $p^{-1}(70)$ ?

Exam 4: Exponential Functions

What is lim⁡t→−∞(14+5e4t−1)\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)limt→−∞​(14+5e4t−1) ? If necessary, enter "inf" for ∞\infty∞ and "-inf" for −∞-\infty−∞ .

A population has size 3,500 at time t=0t=0t=0 , with ttt in years. If the population grows by 80 people per year, what is the formula for PPP , the population at time ttt ?

lim⁡x→∞6e3x=0\lim _{x \rightarrow \infty} 6 e^{3 x}=0limx→∞​6e3x=0

Let P(t)=5,000e0.037tP(t)=5,000 e^{0.037 t}P(t)=5,000e0.037t give the size of a population of animals in year ttt . After how many years will the population be approximately 10,099 ? Round to the nearest year.

Match the graph to its equation.

Is the formula for a function representing a quantity which begins at NNN in year t=0t=0t=0 and grows at a constant annual rate of r%r \%r% given by f(t)=r(1+N)t?f(t)=r(1+N)^{t} ?f(t)=r(1+N)t?

What is the growth factor if sales increase by 37%37 \%37% each month?

Find a possible formula for the exponential function fff such that the points (5,2684.355)(5,2684.355)(5,2684.355) and (3,262.144)(3,262.144)(3,262.144) are on the graph.

Which of the graphs in the following figure is the graph of 150(1.1)t150(1.1)^{t}150(1.1)t ?

The amount of pollution in a harbor ttt hours after it was contaminated by illegal dumping is given by A=50(0.8)tA=50(0.8)^{t}A=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.

Is the function graphed exponential?

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 …(…)t\ldots(\ldots)^{t}…(…)t Round your second answer to 2 decimal places.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%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?

What is lim⁡x→∞e−4x\lim _{x \rightarrow \infty} e^{-4 x}limx→∞​e−4x ? If necessary, enter "inf" for ∞\infty∞ and "-inf" for −∞-\infty−∞ .

An ant population grows at a continuous growth rate of 11.3%11.3 \%11.3% . If the population starts with 22,000 ants, how many ants are there after 6 months? Round your answer to the nearest ant.

The price of an item increases due to inflation. Let p(t) =22.50(1.029) tp(t) =22.50(1.029) ^{t}p(t) =22.50(1.029) t give the price of the item as a function of time in years, with t=0t=0t=0 in 2004. What is the practical interpretation of p−1(70) p^{-1}(70) p−1(70) ?

What is $\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

A population has size 3,500 at time $t=0$ , with $t$ in years. If the population grows by 80 people per year, what is the formula for $P$ , the population at time $t$ ?

$\lim _{x \rightarrow \infty} 6 e^{3 x}=0$

Let $P(t)=5,000 e^{0.037 t}$ give the size of a population of animals in year $t$ . After how many years will the population be approximately 10,099 ? Round to the nearest year.

Match the graph to its equation. $Match the graph to its equation. A) y=-4(1.1) ^{x} B) y=4(1.1) ^{x} C) y=4(0.9) ^{-x} D) y=4(0.9) ^{x}$

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a constant annual rate of $r \%$ given by $f(t)=r(1+N)^{t} ?$

What is the growth factor if sales increase by $37 \%$ each month?

Find a possible formula for the exponential function $f$ such that the points $(5,2684.355)$ and $(3,262.144)$ are on the graph.

Which of the graphs in the following figure is the graph of $150(1.1)^{t}$ ? $Which of the graphs in the following figure is the graph of 150(1.1)^{t} ?$

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=50(0.8)^{t}$ tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ 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?

What is $\lim _{x \rightarrow \infty} e^{-4 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

An ant population grows at a continuous growth rate of $11.3 \%$ . If the population starts with 22,000 ants, how many ants are there after 6 months? Round your answer to the nearest ant.

The price of an item increases due to inflation. Let $p(t) =22.50(1.029) ^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. What is the practical interpretation of $p^{-1}(70)$ ?