Question 1

An investment grows according to the formula $V=7000 e^{0.051 t}$. How many years will it take for the original investment to triple? Round to 1 decimal place.

Accepted Answer

The answer of An investment grows according to the formula...

Question 2

Which of the following characteristics describe the graph of $f(x)=(1.5)^{x}$ ?

Accepted Answer

A)  It is concave down. 
B)  It is concave up. 
C)  It crosses the $y$-axis at 1 . 
D)  As $x \rightarrow \infty, f(x) \rightarrow \infty$. 
E)  As $x \rightarrow \infty, f(x) \rightarrow 0$.
F) As $x \rightarrow-\infty, f(x) \rightarrow \infty$.
G) As $x \rightarrow-\infty, f(x) \rightarrow 0$. 
A)  It is concave down. 
B)  It is concave up. 
C)  It crosses the $y$-axis at 1 . 
D)  As $x \rightarrow \infty, f(x) \rightarrow \infty$. 
E)  As $x \rightarrow \infty, f(x) \rightarrow 0$.
F) As $x \rightarrow-\infty, f(x) \rightarrow \infty$.
G) As $x \rightarrow-\infty, f(x) \rightarrow 0$.

Question 3

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 $g$ ?

Accepted Answer

A) 
  
B) 
  
C) 
  
A) 
  
B) 
  
C)

Question 4

A population has size 3,000 at time $t=0$, with $t$ in years. If the population grows by $10 \%$ per year, what is the formula for $P$, the population at time $t$ ?

Accepted Answer

A)  $ P=3,000(1.1) t$ 
B)  $ P=3,000+10 t$ 
C)  $ P=3,000(1.1)^{t}$ 
D)  $ P=3,000(0.1)^{t}$ 
A)  $ P=3,000(1.1) t$ 
B)  $ P=3,000+10 t$ 
C)  $ P=3,000(1.1)^{t}$ 
D)  $ P=3,000(0.1)^{t}$

Question 5

If you start with $\$ 8,000$, how much money will you have after a $10 \%$ increase?

Accepted Answer

The answer of If you start with $\$ 8,000$, how...

Question 6

For the instantaneous compound interest in the formula $Q=2,500 e^{0.03 t}$, find the effective annual growth rate. Round to the nearest hundredth of a percent.

Accepted Answer

The answer of For the instantaneous compound interest in the...

Question 7

Which of the following is correctly ordered from least to greatest?

Accepted Answer

A)  $e^{4}, \pi^{4}, 2.7^{4}$ 
B)  $\pi^{4}, e^{4}, 2.7^{4}$ 
C)  $e^{4}, 2.7^{4}, \pi^{4}$ 
D)  $\pi^{4}, 2.7^{4}, e^{4}$ 
E)  $2.7^{4}, e^{4}, \pi^{4}$
F) $ 2.7^{4}, \pi^{4}, e^{4}$ 
A)  $e^{4}, \pi^{4}, 2.7^{4}$ 
B)  $\pi^{4}, e^{4}, 2.7^{4}$ 
C)  $e^{4}, 2.7^{4}, \pi^{4}$ 
D)  $\pi^{4}, 2.7^{4}, e^{4}$ 
E)  $2.7^{4}, e^{4}, \pi^{4}$
F) $ 2.7^{4}, \pi^{4}, e^{4}$

Question 8

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=70(0.65)^{t}$ tons. What percentage of the pollution leaves the harbor each hour?

Accepted Answer

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

Question 9

Match the graph to its equation.

Accepted Answer

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)  $y=-1(0.8)^{x}$ 
B)  $y=1(0.8)^{x}$ 
C)  $y=1(1.2)^{-x}$ 
D)  $y=1(1.2)^{x}$

Question 10

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)

Accepted Answer

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

Question 11

The population of a city has been growing at a rate of $4 \%$ per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.

Accepted Answer

The answer of The population of a city has been...

Question 12

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 $P(t)$ be the population of the town $t$ years after 2000 . Use a graph of $P(t)$ to estimate the year in which the population will reach 250,000 .

Accepted Answer

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

Question 13

A store's sales of cassette tapes of music decreased by $6 \%$ 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.

Accepted Answer

The answer of A store's sales of cassette tapes of...

Question 14

For the instantaneous compound interest in the formula $Q=3,000 e^{-0.09 t}$, find the effective annual growth rate. Round to the nearest hundredth of a percent.

Accepted Answer

The answer of For the instantaneous compound interest in the...

Question 15

What is the maximum number of solutions the equation $2+x=2(4)^{x}$ can have?

Accepted Answer

The answer of What is the maximum number of solutions...

Question 16

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a continuous annual rate of $\frac{r}{3} \%$ given by
$f(t)=N e^{\frac{r t}{3}} ?$

Accepted Answer

A) True 
 B)False

Question 17

If you start with $\$ 6,000$, how much money will you have after a $5 \%$ increase followed by a $25 \%$ decrease?

Accepted Answer

The answer of If you start with $\$ 6,000$, how...

Question 18

A population is 30,000 in year $t=0$ and declines at a continuous rate of $5 \%$ per year. What is the formula for $P(t)$, the population in year $t$ ?

Accepted Answer

A)  $P(t)=30,000(5)^{t}$ 
B)  $ P(t)=30,000(0.95)^{t}$ 
C)  $P(t)=30,000 e^{0.95 t}$ 
D)  $ P(t)=30,000 e^{-0.05 t}$ 
A)  $P(t)=30,000(5)^{t}$ 
B)  $ P(t)=30,000(0.95)^{t}$ 
C)  $P(t)=30,000 e^{0.95 t}$ 
D)  $ P(t)=30,000 e^{-0.05 t}$

Question 19

A radioactive substance decays by $12 \%$ every year. Which of the following is the formula for the quantity, $Q$, of a 10 gram sample remaining after $t$ years?

Accepted Answer

A)  $Q=10(0.88)^{t}$ 
B)  $Q=10(1.12)^{t}$ 
C)  $Q=10(-1.12)^{t}$ 
D)  $Q=10(-0.88)^{t}$ 
A)  $Q=10(0.88)^{t}$ 
B)  $Q=10(1.12)^{t}$ 
C)  $Q=10(-1.12)^{t}$ 
D)  $Q=10(-0.88)^{t}$

Question 20

Solve $y=5(1.1)^{x}$ for $x$ if $y=6.655$.

Accepted Answer

The answer of Solve $y=5(1.1)^{x}$ for $x$ if $y=6.655$....

An investment grows according to the formula $V=7000 e^{0.051 t}$ . How many years will it take for the original investment to triple? Round to 1 decimal place.

Which of the following characteristics describe the graph of $f(x)=(1.5)^{x}$ ?

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 $g$ ?

A population has size 3,000 at time $t=0$ , with $t$ in years. If the population grows by $10 \%$ per year, what is the formula for $P$ , the population at time $t$ ?

If you start with $\$ 8,000$ , how much money will you have after a $10 \%$ increase?

For the instantaneous compound interest in the formula $Q=2,500 e^{0.03 t}$ , find the effective annual growth rate. Round to the nearest hundredth of a percent.

Which of the following is correctly ordered from least to greatest?

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=70(0.65)^{t}$ tons. What percentage of the pollution leaves the harbor each hour?

Match the graph to its equation.

The population of a city has been growing at a rate of $4 \%$ per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.

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 $P(t)$ be the population of the town $t$ years after 2000 . Use a graph of $P(t)$ to estimate the year in which the population will reach 250,000 .

A store's sales of cassette tapes of music decreased by $6 \%$ 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.

For the instantaneous compound interest in the formula $Q=3,000 e^{-0.09 t}$ , find the effective annual growth rate. Round to the nearest hundredth of a percent.

What is the maximum number of solutions the equation $2+x=2(4)^{x}$ can have?

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a continuous annual rate of $\frac{r}{3} \%$ given by $f(t)=N e^{\frac{r t}{3}} ?$

If you start with $\$ 6,000$ , how much money will you have after a $5 \%$ increase followed by a $25 \%$ decrease?

A population is 30,000 in year $t=0$ and declines at a continuous rate of $5 \%$ per year. What is the formula for $P(t)$ , the population in year $t$ ?

A radioactive substance decays by $12 \%$ every year. Which of the following is the formula for the quantity, $Q$ , of a 10 gram sample remaining after $t$ years?

Solve $y=5(1.1)^{x}$ for $x$ if $y=6.655$ .

Linear Functions and Change

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Quadratic Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

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Triangle Trigonometry and Polar Coordinates

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Exam 4: Exponential Functions

An investment grows according to the formula V=7000e0.051tV=7000 e^{0.051 t}V=7000e0.051t . How many years will it take for the original investment to triple? Round to 1 decimal place.

Which of the following characteristics describe the graph of f(x)=(1.5)xf(x)=(1.5)^{x}f(x)=(1.5)x ?

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 ggg ?

A population has size 3,000 at time t=0t=0t=0 , with ttt in years. If the population grows by 10%10 \%10% per year, what is the formula for PPP , the population at time ttt ?

If you start with $8,000\$ 8,000$8,000 , how much money will you have after a 10%10 \%10% increase?

For the instantaneous compound interest in the formula Q=2,500e0.03tQ=2,500 e^{0.03 t}Q=2,500e0.03t , find the effective annual growth rate. Round to the nearest hundredth of a percent.

Which of the following is correctly ordered from least to greatest?

The amount of pollution in a harbor ttt hours after it was contaminated by illegal dumping is given by A=70(0.65)tA=70(0.65)^{t}A=70(0.65)t tons. What percentage of the pollution leaves the harbor each hour?

Match the graph to its equation.

The population of a city has been growing at a rate of 4%4 \%4% per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.

A store's sales of cassette tapes of music decreased by 6%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.

For the instantaneous compound interest in the formula Q=3,000e−0.09tQ=3,000 e^{-0.09 t}Q=3,000e−0.09t , find the effective annual growth rate. Round to the nearest hundredth of a percent.

What is the maximum number of solutions the equation 2+x=2(4)x2+x=2(4)^{x}2+x=2(4)x can have?

Is the formula for a function representing a quantity which begins at NNN in year t=0t=0t=0 and grows at a continuous annual rate of r3%\frac{r}{3} \%3r​% given by f(t)=Nert3?f(t)=N e^{\frac{r t}{3}} ?f(t)=Ne3rt​?

If you start with $6,000\$ 6,000$6,000 , how much money will you have after a 5%5 \%5% increase followed by a 25%25 \%25% decrease?

A population is 30,000 in year t=0t=0t=0 and declines at a continuous rate of 5%5 \%5% per year. What is the formula for P(t)P(t)P(t) , the population in year ttt ?

A radioactive substance decays by 12%12 \%12% every year. Which of the following is the formula for the quantity, QQQ , of a 10 gram sample remaining after ttt years?

Solve y=5(1.1)xy=5(1.1)^{x}y=5(1.1)x for xxx if y=6.655y=6.655y=6.655 .

Linear Functions and Change

Functions

Quadratic Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

An investment grows according to the formula $V=7000 e^{0.051 t}$ . How many years will it take for the original investment to triple? Round to 1 decimal place.

Which of the following characteristics describe the graph of $f(x)=(1.5)^{x}$ ?

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 $g$ ?

A population has size 3,000 at time $t=0$ , with $t$ in years. If the population grows by $10 \%$ per year, what is the formula for $P$ , the population at time $t$ ?

If you start with $\$ 8,000$ , how much money will you have after a $10 \%$ increase?

For the instantaneous compound interest in the formula $Q=2,500 e^{0.03 t}$ , find the effective annual growth rate. Round to the nearest hundredth of a percent.

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=70(0.65)^{t}$ tons. What percentage of the pollution leaves the harbor each hour?

The population of a city has been growing at a rate of $4 \%$ per year. If the population was 100,000 in 1990, what was the population in 1995? Round to the nearest whole number.

A store's sales of cassette tapes of music decreased by $6 \%$ 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.

For the instantaneous compound interest in the formula $Q=3,000 e^{-0.09 t}$ , find the effective annual growth rate. Round to the nearest hundredth of a percent.

What is the maximum number of solutions the equation $2+x=2(4)^{x}$ can have?

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a continuous annual rate of $\frac{r}{3} \%$ given by $f(t)=N e^{\frac{r t}{3}} ?$

If you start with $\$ 6,000$ , how much money will you have after a $5 \%$ increase followed by a $25 \%$ decrease?

A population is 30,000 in year $t=0$ and declines at a continuous rate of $5 \%$ per year. What is the formula for $P(t)$ , the population in year $t$ ?

A radioactive substance decays by $12 \%$ every year. Which of the following is the formula for the quantity, $Q$ , of a 10 gram sample remaining after $t$ years?

Solve $y=5(1.1)^{x}$ for $x$ if $y=6.655$ .