Question 1

Is the formula for a function representing a quantity which begins at $4 N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by
$f(t)=4 N e^{r t /100} ?$

Accepted Answer

A) True 
 B)False  True

Question 2

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?

Accepted Answer

exponential

Question 3

The price of an item increases due to inflation. Let $p(t)=32.50(1.047)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.

Accepted Answer

$4.59 \%$

Question 4

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.35$ on day $t$ $=0$ and the price increases by $7 \%$ per day.

Accepted Answer

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

Question 5

For the formula $Q=5,000 e^{0.06 t}$, find the instantaneous growth rate.

Accepted Answer

The answer of For the formula $Q=5,000 e^{0.06 t}$, find...

Question 6

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.38 \%$ per year. How many million people would you expect to live in the United States in the year 2020? Round to 1 decimal place.

Accepted Answer

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

Question 7

Let $\left(t_{0}, P\left(t_{0}\right)\right)$ be the intersection of the graphs of the two exponential functions $P=a(1+r)^{t}$ and $P=b(1+s)^{t}$, where $0<a<b$. If $r$ is increased, does $P\left(t_{0}\right)$ increase, decrease, or stay the same?

Accepted Answer

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

Question 8

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 $h$ ?

Accepted Answer

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

Question 9

Which of the following quantities $Q$ are increasing with time $t$ ?

Accepted Answer

A)  $Q=-4 e^{0.3 t}$ 
B)  $Q=-4 e^{-0.3 t}$ 
C)  $Q=-4(1.3)^{t}$ 
D)  $Q=-4(0.7)^{t}$ 
A)  $Q=-4 e^{0.3 t}$ 
B)  $Q=-4 e^{-0.3 t}$ 
C)  $Q=-4(1.3)^{t}$ 
D)  $Q=-4(0.7)^{t}$

Question 10

Solve $y=18(0.84)^{x}$ graphically for $x$ if $y=13$. Round to 2 decimal places.

Accepted Answer

The answer of Solve $y=18(0.84)^{x}$ graphically for $x$ if $y=13$....

Question 11

A population is 150,000 in year $t=0$ and declines at a continuous rate of $8 \%$ per year. By what percentage does the population decrease each year? Round to 2 decimal places.

Accepted Answer

The answer of A population is 150,000 in year $t=0$...

Question 12

Which of the following formulas are exponential?

Accepted Answer

A)  $ P(t)=8.9(1.21)^{t}$ 
B)  $ P(t)=1.89-9.68 t$ 
C)  $ P(t)=17.8^{t}+40.05 t-22.25$ 
D)  $ P(t)=(1.4641)^{t} 2670$ 
E)  $ P(t)=178 e^{2.42 t}$
F) $ P(t)=1.78 e^{-0.605 t}$
G) $ P(t)=(4.45+12.1 t)^{t}$ 
A)  $ P(t)=8.9(1.21)^{t}$ 
B)  $ P(t)=1.89-9.68 t$ 
C)  $ P(t)=17.8^{t}+40.05 t-22.25$ 
D)  $ P(t)=(1.4641)^{t} 2670$ 
E)  $ P(t)=178 e^{2.42 t}$
F) $ P(t)=1.78 e^{-0.605 t}$
G) $ P(t)=(4.45+12.1 t)^{t}$

Question 13

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)  $y=4(0.9)^{x}$ 
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 14

Which equation has a rate of change of $9 \%$ ?

Accepted Answer

A)  $Q=(3,200) 0.91^{t}$ 
B)  $Q=(3,200) 109^{t}$ 
C)  $ Q=(3,200) 1.09^{t}$ 
D)  $Q=(3,200) 91^{t}$ 
A)  $Q=(3,200) 0.91^{t}$ 
B)  $Q=(3,200) 109^{t}$ 
C)  $ Q=(3,200) 1.09^{t}$ 
D)  $Q=(3,200) 91^{t}$

Question 15

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?

Accepted Answer

The answer of Consider the following figure, where Graph I...

Question 16

Without a calculator, graph the following on the same set of axes:
A) $e^{x}$
B) $e^{2 x}$
C) $e^{-2 x}$

Accepted Answer

The answer of Without a calculator, graph the following on...

Question 17

The graph of the exponential function $P(t)$ is shown below. The formula for $p(t)=\ldots(\ldots)^{t}$

Accepted Answer

Part A: 62

Question 18

The populations of 4 species of animals are given by the following equations:
$P_{1}=650(0.71)^{t} P_{2}=600(1.2)^{t} P_{3}=270(0.88)^{t} P_{4}=610(1.05)^{t}$
Which species are shrinking in size?

Accepted Answer

A)  $P_{4}$ 
B)  $P_{3}$ 
C)  $P_{2}$ 
D)  $P_{1}$ 
A)  $P_{4}$ 
B)  $P_{3}$ 
C)  $P_{2}$ 
D)  $P_{1}$

Question 19

The populations of 4 species of animals are given by the following equations:
$P_{1}=470(0.81)^{t} P_{2}=900(1.28)^{t} P_{3}=670(0.73)^{t} P_{4}=640(1.05)^{t}$
What is the annual percent growth rate for the population that is growing the fastest?

Accepted Answer

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

Question 20

One solution to the equation $3+x=3(2)^{x}$ is $x=0$. Use your calculator to estimate the other solution to 2 decimal places.

Accepted Answer

The answer of One solution to the equation $3+x=3(2)^{x}$ is...

Is the formula for a function representing a quantity which begins at $4 N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by $f(t)=4 N e^{r t /100} ?$

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?

The price of an item increases due to inflation. Let $p(t)=32.50(1.047)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.35$ on day $t$ $=0$ and the price increases by $7 \%$ per day.

For the formula $Q=5,000 e^{0.06 t}$ , find the instantaneous growth rate.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.38 \%$ per year. How many million people would you expect to live in the United States in the year 2020? Round to 1 decimal place.

Let $\left(t_{0}, P\left(t_{0}\right)\right)$ be the intersection of the graphs of the two exponential functions $P=a(1+r)^{t}$ and $P=b(1+s)^{t}$ , where $0<a<b$ . If $r$ is increased, does $P\left(t_{0}\right)$ increase, decrease, or stay the same?

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 of the following quantities $Q$ are increasing with time $t$ ?

Solve $y=18(0.84)^{x}$ graphically for $x$ if $y=13$ . Round to 2 decimal places.

A population is 150,000 in year $t=0$ and declines at a continuous rate of $8 \%$ per year. By what percentage does the population decrease each year? Round to 2 decimal places.

Which of the following formulas are exponential?

Match the graph to its equation.

Which equation has a rate of change of $9 \%$ ?

Without a calculator, graph the following on the same set of axes: A) $e^{x}$ B) $e^{2 x}$ C) $e^{-2 x}$

The graph of the exponential function $P(t)$ is shown below. The formula for $p(t)=\ldots(\ldots)^{t}$ $The graph of the exponential function P(t) is shown below. The formula for p(t)=\ldots(\ldots)^{t}$

The populations of 4 species of animals are given by the following equations: $P_{1}=650(0.71)^{t} P_{2}=600(1.2)^{t} P_{3}=270(0.88)^{t} P_{4}=610(1.05)^{t}$ Which species are shrinking in size?

The populations of 4 species of animals are given by the following equations: $P_{1}=470(0.81)^{t} P_{2}=900(1.28)^{t} P_{3}=670(0.73)^{t} P_{4}=640(1.05)^{t}$ What is the annual percent growth rate for the population that is growing the fastest?

One solution to the equation $3+x=3(2)^{x}$ is $x=0$ . Use your calculator to estimate the other solution to 2 decimal places.

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

Exam 4: Exponential Functions

Is the formula for a function representing a quantity which begins at 4N4 N4N in year t=0t=0t=0 and grows at a continuous annual rate of r%r \%r% given by f(t)=4Nert/100?f(t)=4 N e^{r t /100} ?f(t)=4Nert/100?

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?

The price of an item increases due to inflation. Let p(t)=32.50(1.047)tp(t)=32.50(1.047)^{t}p(t)=32.50(1.047)t give the price of the item as a function of time in years, with t=0t=0t=0 in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.

Write the formula for the price ppp of a gallon of gas in ttt days if the price is $3.35\$ 3.35$3.35 on day ttt =0=0=0 and the price increases by 7%7 \%7% per day.

For the formula Q=5,000e0.06tQ=5,000 e^{0.06 t}Q=5,000e0.06t , find the instantaneous growth rate.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.38%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.

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,gf, gf,g , or hhh ?

Which of the following quantities QQQ are increasing with time ttt ?

Solve y=18(0.84)xy=18(0.84)^{x}y=18(0.84)x graphically for xxx if y=13y=13y=13 . Round to 2 decimal places.

A population is 150,000 in year t=0t=0t=0 and declines at a continuous rate of 8%8 \%8% per year. By what percentage does the population decrease each year? Round to 2 decimal places.

Which of the following formulas are exponential?

Match the graph to its equation.

Which equation has a rate of change of 9%9 \%9% ?

Without a calculator, graph the following on the same set of axes: A) exe^{x}ex B) e2xe^{2 x}e2x C) e−2xe^{-2 x}e−2x

The graph of the exponential function P(t)P(t)P(t) is shown below. The formula for p(t)=…(…)tp(t)=\ldots(\ldots)^{t}p(t)=…(…)t

One solution to the equation 3+x=3(2)x3+x=3(2)^{x}3+x=3(2)x is x=0x=0x=0 . Use your calculator to estimate the other solution to 2 decimal places.

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

Is the formula for a function representing a quantity which begins at $4 N$ in year $t=0$ and grows at a continuous annual rate of $r \%$ given by $f(t)=4 N e^{r t /100} ?$

The price of an item increases due to inflation. Let $p(t)=32.50(1.047)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. At what continuous annual rate is the price increasing? Round to 2 decimal places.

Write the formula for the price $p$ of a gallon of gas in $t$ days if the price is $\$ 3.35$ on day $t$ $=0$ and the price increases by $7 \%$ per day.

For the formula $Q=5,000 e^{0.06 t}$ , find the instantaneous growth rate.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.38 \%$ per year. How many million people would you expect to live in the United States in the year 2020? Round to 1 decimal place.

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 of the following quantities $Q$ are increasing with time $t$ ?

Solve $y=18(0.84)^{x}$ graphically for $x$ if $y=13$ . Round to 2 decimal places.

A population is 150,000 in year $t=0$ and declines at a continuous rate of $8 \%$ per year. By what percentage does the population decrease each year? Round to 2 decimal places.

Which equation has a rate of change of $9 \%$ ?

Without a calculator, graph the following on the same set of axes: A) $e^{x}$ B) $e^{2 x}$ C) $e^{-2 x}$

The graph of the exponential function $P(t)$ is shown below. The formula for $p(t)=\ldots(\ldots)^{t}$ $The graph of the exponential function P(t) is shown below. The formula for p(t)=\ldots(\ldots)^{t}$

One solution to the equation $3+x=3(2)^{x}$ is $x=0$ . Use your calculator to estimate the other solution to 2 decimal places.