Question 1

Approximate the number using a calculator. Round your answer to three decimal places.
-The rabbit population in a forest area grows at the rate of $9 \%$ monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use $y = 160 ( 2.7 ) ^ { 0.09 t }$
A) 468
B) 467
C) 481
D) 455

Accepted Answer

The formula given is $y = 160(2.7)^{0.09t}$, where $t$ is the time in months. Since we're looking from July to next July, $t = 12$ months. Plugging the values into the formula gives $y = 160(2.7)^{0.09 \times 12}$. Calculating this yields $y \approx 468$, hence the nearest whole number of rabbits expected by next July is 468.

Question 2

Graph the function by making a table of coordinates.
-$f(x)=\left(\frac{1}{4}\right)^{x}$

A)

B)

C)

D)

Accepted Answer

A

Question 3

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = 3 ^ { x } - 2$
B) $f ( x ) = 3 ^ { x }$
C) $f ( x ) = 3 ^ { x - 2 }$
D) $f ( x ) = 3 ^ { x } + 2$

Accepted Answer

A

Question 4

Approximate the number using a calculator. Round your answer to three decimal places.
-$4 ^ { - 2.9 }$
A) $0.018$
B) $- 11.600$
C) $70.728$
D) $0.318$

Accepted Answer

Using a calculator to compute $4^{-2.9}$ and rounding to three decimal places gives approximately 0.018.

Question 5

Graph the function by making a table of coordinates.
-$$f ( x ) = 0.7 ^ { x }$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the function by making a table...

Question 6

Graph the function by making a table of coordinates.
-$f(x)=5^{x}$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the function by making a table...

Question 7

Graph the function
-Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$.

A)

B)

C)

D)

Accepted Answer

The answer of Graph the function
-Use the graph of \(f...

Question 8

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = - 5 ^ { - x }$
B) $f ( x ) = 5 ^ { x }$
C) $f ( x ) = - 5 ^ { x }$
D) $f ( x ) = 5 ^ { - x }$ .

Accepted Answer

The answer of The graph of an exponential function is...

Question 9

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = - 3 ^ { x }$
B) $f ( x ) = 3 ^ { x }$
C) $f ( x ) = 3 ^ { - x }$
D) $f ( x ) = - 3 ^ { - x }$

Accepted Answer

The answer of The graph of an exponential function is...

Question 10

Approximate the number using a calculator. Round your answer to three decimal places.
-The formula $S = A \left( \frac { ( 1 + r ) ^ { t + 1 } - 1 } { r } \right)$ models the value of a retirement account, where $A =$ the number of dollars added to the retirement account each year, $\mathrm { r } =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement account after t years. If the interest rate is $6 \%$, how much will the account be worth after 15 years if $\$ 400$ is added each year? Round to the nearest whole number.
A) $\$ 10,269$
B) $\$ 999$
C) $\$ 6400$
D) $\$ 15,338$

Accepted Answer

Using the given formula and plugging in the values $A = 400$, $r = 0.06$, and $t = 15$, the calculation yields approximately \$10,269 when rounded to the nearest whole number.

Question 11

Graph the function
-Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 1$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the function
-Use the graph of \(f...

Question 12

Approximate the number using a calculator. Round your answer to three decimal places.
-$6 ^ { 3.6 }$
A) $632.914$
B) $21.600$
C) $2176.782$
D) $633.214$

Accepted Answer

Using a calculator to compute $6^{3.6}$, the result is approximately 632.955, which when rounded to three decimal places is 632.914.

Question 13

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = 5 ^ { x - 1 }$
B) $f ( x ) = 5 ^ { x }$
C) $f ( x ) = 5 ^ { x } - 1$
D) $f ( x ) = 5 ^ { x } + 1$

Accepted Answer

The answer of The graph of an exponential function is...

Question 14

Approximate the number using a calculator. Round your answer to three decimal places.
-A city is growing at the rate of $0.7 \%$ annually. If there were $3,767,000$ residents in the city in 1992, find how many (to the nearest ten-thousand) are living in that city in 2000 . Use $y = 3,767,000 ( 2.7 ) = .007 \mathrm { t }$.
A) $3,980,000$
B) 570,000
C) $10,170,000$
D) $4,010,000$

Accepted Answer

The given formula seems incorrect for calculating population growth. The correct approach to calculate the population after a certain number of years with an annual growth rate is using the formula $P = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate, and $t$ is the number of years. For a growth rate of 0.7% or 0.007 as a decimal, an initial population of 3,767,000, and a time span of 8 years (from 1992 to 2000), the calculation should be $3,767,000(1 + 0.007)^8$. This calculation gives a result close to 3,980,000 when rounded to the nearest ten-thousand.

Question 15

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = 2 ^ { x }$
B) $f ( x ) = 2 ^ { x + 1 }$
C) $f ( x ) = 2 ^ { x } + 1$
D) $f ( x ) = 2 ^ { x } - 1$

Accepted Answer

The answer of The graph of an exponential function is...

Question 16

Approximate the number using a calculator. Round your answer to three decimal places.
-$4 ^ { \pi }$
A) $77.880$
B) $97.409$
C) $12.566$
D) $36.462$

Accepted Answer

The answer of Approximate the number using a calculator. Round...

Question 17

Approximate the number using a calculator. Round your answer to three decimal places.
-$6 ^{\sqrt { 2 }}$
A) $12.603$
B) $8.485$
C) $8.000$
D) $18.000$

Accepted Answer

The answer of Approximate the number using a calculator. Round...

Question 18

Graph the function by making a table of coordinates.
-$f(x)=\left(\frac{3}{2}\right)^{x}$

A)

B)

C)

Accepted Answer

The answer of Graph the function by making a table...

Question 19

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-
A) $f ( x ) = 2 ^ { - x }$
B) $f ( x ) = 2 ^ { x }$
C) $f ( x ) = - 2 ^ { x }$
D) $f ( x ) = - 2 ^ { - x }$

Accepted Answer

The answer of The graph of an exponential function is...

Question 20

Approximate the number using a calculator. Round your answer to three decimal places.
-The function $f ( x ) = 500 ( 0.5 ) ^ { x / 100 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.
A) 189 pounds
B) 305 pounds
C) 350 pounds
D) 179 pounds

Accepted Answer

The function $f(x) = 500 (0.5)^{x/100}$ is used to find the amount after 140 years: $f(140) = 500 (0.5)^{140/100} \approx 189.207$. Rounded to the nearest whole number, it is 189 pounds.

Quiz 4: Exponential and Logarithmic Functions

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{1}{4}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{1}{4}\right) ^{x} A) B) C) D)$

Approximate the number using a calculator. Round your answer to three decimal places. - $4 ^ { - 2.9 }$

Graph the function by making a table of coordinates. - $f ( x ) = 0.7 ^ { x }$ $Graph the function by making a table of coordinates. - f ( x ) = 0.7 ^ { x } A) B) C) D)$

Graph the function by making a table of coordinates. - $f(x) =5^{x}$ $Graph the function by making a table of coordinates. - f(x) =5^{x} A) B) C) D)$

Graph the function -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$ . $Graph the function -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 ^ { x - 4 } . A) B) C) D)$

Graph the function -Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 1$ $Graph the function -Use the graph of f ( x ) = 5 ^ { x } to obtain the graph of g ( x ) = 5 ^ { x } + 1 A) B) C) D)$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^ { 3.6 }$

Approximate the number using a calculator. Round your answer to three decimal places. - $4 ^ { \pi }$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^{\sqrt { 2 }}$

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{3}{2}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{3}{2}\right) ^{x} A) B) C)$

Quiz 4: Exponential and Logarithmic Functions

Graph the function by making a table of coordinates. - f(x) =(14) xf(x) =\left(\frac{1}{4}\right) ^{x}f(x) =(41​) x

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Approximate the number using a calculator. Round your answer to three decimal places. - 4−2.94 ^ { - 2.9 }4−2.9

Graph the function by making a table of coordinates. - f(x) =0.7xf ( x ) = 0.7 ^ { x }f(x) =0.7x

Graph the function by making a table of coordinates. - f(x) =5xf(x) =5^{x}f(x) =5x

Graph the function -Use the graph of f(x) =2xf ( x ) = 2 ^ { x }f(x) =2x to obtain the graph of g(x) =2x−4g ( x ) = 2 ^ { x - 4 }g(x) =2x−4 .

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function -Use the graph of f(x) =5xf ( x ) = 5 ^ { x }f(x) =5x to obtain the graph of g(x) =5x+1g ( x ) = 5 ^ { x } + 1g(x) =5x+1

Approximate the number using a calculator. Round your answer to three decimal places. - 63.66 ^ { 3.6 }63.6

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Approximate the number using a calculator. Round your answer to three decimal places. - 4π4 ^ { \pi }4π

Approximate the number using a calculator. Round your answer to three decimal places. - 626 ^{\sqrt { 2 }}62​

Graph the function by making a table of coordinates. - f(x) =(32) xf(x) =\left(\frac{3}{2}\right) ^{x}f(x) =(23​) x

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{1}{4}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{1}{4}\right) ^{x} A) B) C) D)$

Approximate the number using a calculator. Round your answer to three decimal places. - $4 ^ { - 2.9 }$

Graph the function by making a table of coordinates. - $f ( x ) = 0.7 ^ { x }$ $Graph the function by making a table of coordinates. - f ( x ) = 0.7 ^ { x } A) B) C) D)$

Graph the function by making a table of coordinates. - $f(x) =5^{x}$ $Graph the function by making a table of coordinates. - f(x) =5^{x} A) B) C) D)$

Graph the function -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$ . $Graph the function -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 ^ { x - 4 } . A) B) C) D)$

Graph the function -Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 1$ $Graph the function -Use the graph of f ( x ) = 5 ^ { x } to obtain the graph of g ( x ) = 5 ^ { x } + 1 A) B) C) D)$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^ { 3.6 }$

Approximate the number using a calculator. Round your answer to three decimal places. - $4 ^ { \pi }$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^{\sqrt { 2 }}$

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{3}{2}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{3}{2}\right) ^{x} A) B) C)$