Question 1

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.

Accepted Answer

The answer of The table below shows $v$, the dollar...

Question 2

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".

Accepted Answer

The answer of Assume that all important features are shown...

Question 3

Let $P(t)=4,500 e^{0.043 t}$ give the size of a population of animals in year $t$. What will the population be after 12 years? Round to the nearest whole number.

Accepted Answer

The answer of Let $P(t)=4,500 e^{0.043 t}$ give the size...

Question 4

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 $P(t)$, the population of the town $t$ years after 2000 , is given by $p(t)=\ldots(\ldots)^{t}$.Round your second answer to 3 decimal places.

Accepted Answer

The answer of The population of a city is increasing...

Question 5

Let $\left(x_{0}, y_{0}\right)$ be the intersection of the graphs of the two exponential functions $y=a e^{b x}$ and $y=c e^{d x}$, where $0<a<c$. If $a$ is increased, does $x_{0}$ increase, decrease, or stay the same?

Accepted Answer

The answer of Let $\left(x_{0}, y_{0}\right)$ be the intersection of...

Question 6

Kevin buys a new CD player for $\$ 300$, and finds two years later when he wants to sell it that it is only worth $\$ 82$. Assuming the value of the CD player decreases exponentially, the formula for $V(t)$, the value of the CD player after $t$ years, is given by $V(t)=\ldots(\ldots)^{t}$. Round your second answer to 2 decimal places.

Accepted Answer

The answer of Kevin buys a new CD player for...

Question 7

Is the formula for a function representing a quantity which begins at an amount $35 \%$ larger than $N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by $f(t)=1.35 N e^{r t /100}$ ?

Accepted Answer

A) True 
 B)False

Question 8

What is $\lim _{x \rightarrow \infty}-5 e^{3 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$.

Accepted Answer

The answer of What is \(\lim _{x \rightarrow \infty}-5 e^{3...

Question 9

The populations of 4 species of animals are given by the following equations:
$P_{1}=390(0.75)^{t} P_{2}=100(1.09)^{t} P_{3}=230(0.82)^{t} P_{4}=600(1.05)^{t}$
What is the largest initial population of the 4 species?

Accepted Answer

The answer of The populations of 4 species of animals...

Question 10

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 $b$ ?

Accepted Answer

The answer of In the following figure, the functions \(f,...

Question 11

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= ------------

Accepted Answer

The answer of The following table gives values from an...

Question 12

Is the function graphed exponential?

Accepted Answer

A) True 
 B)False

Question 13

Find $\lim _{t \rightarrow \infty} 20,000(0.82)^{t}$. For $\infty$ or $-\infty$, enter "inf" or "-inf".

Accepted Answer

The answer of Find $\lim _{t \rightarrow \infty} 20,000(0.82)^{t}$. For...

Question 14

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?

Accepted Answer

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 15

In 2006, the cost of a particular piece of computer equipment was $\$ 490$ and going down at a rate of $14 \%$ per year. Assuming this percentage remains constant, what is the formula for $C$, the cost of this equipment in dollars, as a function of $t$, the number of years since 2006 ?

Accepted Answer

A)  $ C=490(0.86)^{t}$ 
B)  $ C=490(-1.14)^{t}$ 
C)  $ C=490(0.14)^{t}$ 
D)  $ C=490(-0.86)^{t}$

Question 16

The price of an item increases due to inflation. Let $p(t)=12.50(1.024)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004 . Estimate $p^{-1}(75)$ to 2 decimal places.

Accepted Answer

The answer of The price of an item increases due...

Question 17

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is exponential.

Accepted Answer

The answer of Let $f(x)$ be given in the table...

Question 18

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.85$ on day $t$ $=0$ and the price increases by $\$ 0.08$ per day.

Accepted Answer

The answer of Write the formula for the price $p$...

Question 19

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 $Q$, 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 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 $Q(t)=\ldots(\ldots)^{t}$. Round both answers to 3 decimal places.

Accepted Answer

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

Question 20

The graph of $P(t)=1.7^{-t}+29$ has a horizontal asymptote at $P(t)=$ ---------. (If there is no horizontal asymptote, enter "DNE".)

Accepted Answer

The answer of The graph of $P(t)=1.7^{-t}+29$ has a horizontal...

Exam 4: Exponential Functions

Let $P(t)=4,500 e^{0.043 t}$ give the size of a population of animals in year $t$ . What will the population be after 12 years? Round to the nearest whole number.

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 $P(t)$ , the population of the town $t$ years after 2000 , is given by $p(t)=\ldots(\ldots)^{t}$ .Round your second answer to 3 decimal places.

Let $\left(x_{0}, y_{0}\right)$ be the intersection of the graphs of the two exponential functions $y=a e^{b x}$ and $y=c e^{d x}$ , where $0<a<c$ . If $a$ is increased, does $x_{0}$ increase, decrease, or stay the same?

Is the formula for a function representing a quantity which begins at an amount $35 \%$ larger than $N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by $f(t)=1.35 N e^{r t /100}$ ?

What is $\lim _{x \rightarrow \infty}-5 e^{3 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

The populations of 4 species of animals are given by the following equations: $P_{1}=390(0.75)^{t} P_{2}=100(1.09)^{t} P_{3}=230(0.82)^{t} P_{4}=600(1.05)^{t}$ What is the largest initial population of the 4 species?

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 $b$ ? $In the following figure, the functions f, g, h , and p can all be written in the form y=a b^{t} . Which one has the largest value for b ?$

Is the function graphed exponential?

Find $\lim _{t \rightarrow \infty} 20,000(0.82)^{t}$ . For $\infty$ or $-\infty$ , enter "inf" or "-inf".

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?

In 2006, the cost of a particular piece of computer equipment was $\$ 490$ and going down at a rate of $14 \%$ per year. Assuming this percentage remains constant, what is the formula for $C$ , the cost of this equipment in dollars, as a function of $t$ , the number of years since 2006 ?

The price of an item increases due to inflation. Let $p(t)=12.50(1.024)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004 . Estimate $p^{-1}(75)$ to 2 decimal places.

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is exponential.

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.85$ on day $t$ $=0$ and the price increases by $\$ 0.08$ per day.

The graph of $P(t)=1.7^{-t}+29$ has a horizontal asymptote at $P(t)=$ ---------. (If there is no horizontal asymptote, enter "DNE".)

Exam 4: Exponential Functions

The table below shows vvv , the dollar value of a share of a certain stock, as a function of ttt , the time (in weeks) since the initial offering of the stock. A possible formula for v(t)v(t)v(t) is v(t)=…(…)tv(t)=\ldots(\ldots)^{t}v(t)=…(…)t . Round the second answer to 3 decimal places.

Assume that all important features are shown in the following graph of y=f(x)y=f(x)y=f(x) . What is lim⁡x→−∞f(x)\lim _{x \rightarrow-\infty} f(x)limx→−∞​f(x) ? For ∞\infty∞ or −∞-\infty−∞ , enter "inf" or "-inf".

Let P(t)=4,500e0.043tP(t)=4,500 e^{0.043 t}P(t)=4,500e0.043t give the size of a population of animals in year ttt . What will the population be after 12 years? Round to the nearest whole number.

Let (x0,y0)\left(x_{0}, y_{0}\right)(x0​,y0​) be the intersection of the graphs of the two exponential functions y=aebxy=a e^{b x}y=aebx and y=cedxy=c e^{d x}y=cedx , where 0<a<c0<a<c0<a<c . If aaa is increased, does x0x_{0}x0​ increase, decrease, or stay the same?

Is the formula for a function representing a quantity which begins at an amount 35%35 \%35% larger than NNN in year t=0t=0t=0 and grows at a continuous annual rate of r%r \%r% given by f(t)=1.35Nert/100f(t)=1.35 N e^{r t /100}f(t)=1.35Nert/100 ?

What is lim⁡x→∞−5e3x\lim _{x \rightarrow \infty}-5 e^{3 x}limx→∞​−5e3x ? If necessary, enter "inf" for ∞\infty∞ and "-inf" for −∞-\infty−∞ .

In the following figure, the functions f,g,hf, g, hf,g,h , and ppp can all be written in the form y=abty=a b^{t}y=abt . Which one has the largest value for bbb ?

The following table gives values from an exponential or a linear function. Determine which, and find values for aaa and bbb so that f(x)=a+bxf(x)=a+b xf(x)=a+bx if the function is linear, or f(x)=a(b)xf(x)=a(b)^{x}f(x)=a(b)x if the function is exponential. a= ---------------,b= ------------

Is the function graphed exponential?

Find lim⁡t→∞20,000(0.82)t\lim _{t \rightarrow \infty} 20,000(0.82)^{t}limt→∞​20,000(0.82)t . For ∞\infty∞ or −∞-\infty−∞ , enter "inf" or "-inf".

The graph below shows the quantity of a drug in a patient's bloodstream over a period of time ttt , in minutes. Which of the following scenarios best describes the graph?

In 2006, the cost of a particular piece of computer equipment was $490\$ 490$490 and going down at a rate of 14%14 \%14% per year. Assuming this percentage remains constant, what is the formula for CCC , the cost of this equipment in dollars, as a function of ttt , the number of years since 2006 ?

The price of an item increases due to inflation. Let p(t)=12.50(1.024)tp(t)=12.50(1.024)^{t}p(t)=12.50(1.024)t give the price of the item as a function of time in years, with t=0t=0t=0 in 2004 . Estimate p−1(75)p^{-1}(75)p−1(75) to 2 decimal places.

Let f(x)f(x)f(x) be given in the table below. Find the value of kkk if f(x)f(x)f(x) is exponential.

Write the formula for the price ppp of a gallon of gas in ttt days if the price is $3.85\$ 3.85$3.85 on day ttt =0=0=0 and the price increases by $0.08\$ 0.08$0.08 per day.

The graph of P(t)=1.7−t+29P(t)=1.7^{-t}+29P(t)=1.7−t+29 has a horizontal asymptote at P(t)=P(t)=P(t)= ---------. (If there is no horizontal asymptote, enter "DNE".)

Let $P(t)=4,500 e^{0.043 t}$ give the size of a population of animals in year $t$ . What will the population be after 12 years? Round to the nearest whole number.

Let $\left(x_{0}, y_{0}\right)$ be the intersection of the graphs of the two exponential functions $y=a e^{b x}$ and $y=c e^{d x}$ , where $0<a<c$ . If $a$ is increased, does $x_{0}$ increase, decrease, or stay the same?

Is the formula for a function representing a quantity which begins at an amount $35 \%$ larger than $N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by $f(t)=1.35 N e^{r t /100}$ ?

What is $\lim _{x \rightarrow \infty}-5 e^{3 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

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 $b$ ? $In the following figure, the functions f, g, h , and p can all be written in the form y=a b^{t} . Which one has the largest value for b ?$

Find $\lim _{t \rightarrow \infty} 20,000(0.82)^{t}$ . For $\infty$ or $-\infty$ , enter "inf" or "-inf".

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?

In 2006, the cost of a particular piece of computer equipment was $\$ 490$ and going down at a rate of $14 \%$ per year. Assuming this percentage remains constant, what is the formula for $C$ , the cost of this equipment in dollars, as a function of $t$ , the number of years since 2006 ?

The price of an item increases due to inflation. Let $p(t)=12.50(1.024)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004 . Estimate $p^{-1}(75)$ to 2 decimal places.

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is exponential.

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.85$ on day $t$ $=0$ and the price increases by $\$ 0.08$ per day.

The graph of $P(t)=1.7^{-t}+29$ has a horizontal asymptote at $P(t)=$ ---------. (If there is no horizontal asymptote, enter "DNE".)