Question 1

Solve the problem.
-The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm { D } ( \mathrm { x } ) = 4700 ( 5 ) ^ { \mathrm { x } }$, where $\mathrm { x }$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $x = 0$ and $x = 3$.
A) $4700 ; 14,687,500$
B) $4700 ; 70,500$
C) $4700 ; 587,500$
D) 23,$500 ; 587,500$

Accepted Answer

C

Question 2

Graph.
-$f(x)=4^{3 x-2}$

A)

B)

C)

D)

Accepted Answer

C

Question 3

Graph.
-$f(x)=\left(\frac{1}{2}\right)^{x}$

A)

B)

C)

D)

Accepted Answer

A

Question 4

Solve the problem.
-The half-life of a certain radioactive substance is 22 years. Suppose that at time $t = 0$, there are $24 \mathrm {~g}$ of the substance. Then after t years, the number of grams of the substance remaining will be:
$N ( t ) = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 44 }$
How many grams of the substance will remain after 242 years? Round to the nearest hundredth when necessary.
A) $0.53 \mathrm {~g}$
B) $0.07 \mathrm {~g}$
C) $0.27 \mathrm {~g}$
D) $0.13 \mathrm {~g}$

Accepted Answer

The half-life of the substance is 22 years, so after 242 years, the substance will have gone through 242/22 = 11 half-lives. Each half-life reduces the amount of substance by half, so after 11 half-lives, only 1/2^11 = 0.000488 of the original amount will remain. Therefore, after 242 years, there will be 24 * 0.000488 = 0.0117 grams of the substance remaining, which rounds to 0.01 grams.

Question 5

Solve the problem.
-The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$, where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$.
A) 10,$600 ; 169,600$
B) $5300 ; 21,200$
C) $5300 ; 169,600$
D) $5300 ; 53,000$

Accepted Answer

When $x = 0$, $B(x) = 5300(2)^0 = 5300$. When $x = 5$, $B(x) = 5300(2)^5 = 5300 \times 32 = 169,600$.

Question 6

Solve the problem.
-The amount of particulate matter left in solution during a filtering process decreases by the equation $P ( n ) = 600 ( 0.5 ) ^ { 0.8 n }$, where $n$ is the number of filtering steps. Find the amounts left for $n = 0$ and $n = 5$. (Round to the nearest whole number.)
A) $1200 ; 38$
B) $600 ; 19$
C) $600 ; 9600$
D) $600 ; 38$

Accepted Answer

For $n = 0$, $P(0) = 600(0.5)^{0.8(0)} = 600(1) = 600$. For $n = 5$, $P(5) = 600(0.5)^{0.8(5)} \approx 600(0.5)^4 \approx 600(0.0625) \approx 37.5$, which rounds to 38.

Question 7

Graph.
-$f(x)=4^{x-4}$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$f(x)=4^{x-4}$

A)

B)

C)

D)

...

Question 8

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:
 
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year $2002 .$

A) About $\$ 1,000,000$
B) About $\$ 1,700,000$
C) About $\$ 750,000$
D) About $\$ 1,300,000$

Accepted Answer

The answer of Solve the problem.
-An accountant tabulated a firm's...

Question 9

Graph.
-$f(x)=\left(\frac{1}{4}\right)^{x}+3$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$f(x)=\left(\frac{1}{4}\right)^{x}+3$

A)

B)

C)

D)

...

Question 10

Graph.
-$f(x)=3^{-x}$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$f(x)=3^{-x}$

A)

B)

C)

D)

...

Question 11

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year $2002 .$

A) About $\$ 500,000$
B) About $\$ 900,000$
C) About $\$ 800,000$
D) About $\$ 1,000,000$

Accepted Answer

The answer of Solve the problem.
-An accountant tabulated a firm's...

Question 12

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year $2001 .$

A) About $\$ 1,300,000$
B) About $\$ 300,000$
C) About $\$ 1,000,000$
D) About $\$ 750,000$

Accepted Answer

The answer of Solve the problem.
-An accountant tabulated a firm's...

Question 13

Solve the problem.
-A computer is purchased for $\$ 4700$. Its value each year is about $78 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $\mathrm { V } ( \mathrm { t } ) = 4700 ( 0.78 ) ^ { \mathrm { t } }$. Find the value of the computer after 7 years.
A) $\$ 643.95$
B) $\$ 502.28$
C) $\$ 825.58$
D) $\$ 25,662.00$

Accepted Answer

The answer of Solve the problem.
-A computer is purchased for...

Question 14

Solve the problem.
-The half-life of Antimony 111 is $2.9$ hours. If the formula $\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { t / 2.9 }$ gives the percent (as a decimal) remaining after time $t$ (in hours), sketch P versus $t$.

A)

B)

C)

D)

Accepted Answer

The answer of Solve the problem.
-The half-life of Antimony 111...

Question 15

Graph.
-$f(x)= 3^{x}$ 
A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$f(x)= 3^{x}$ 
A)

B)

C)

D)

...

Question 16

Graph.
-$x=\left(\frac{1}{2}\right)^{y}$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$x=\left(\frac{1}{2}\right)^{y}$

A)

B)

C)

D)

...

Question 17

Graph.
-$$x = 6 y$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-$$x = 6 y$$

A)

B)

C)

D)

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Question 18

Graph.
-$$f ( x ) = 3 ^ { x } - 2$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph.
-\[f ( x ) = 3 ^...

Question 19

Solve the problem.
-Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years. 
A) $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ( 1.04 ) ^ { \mathrm { t } }$
B) $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ( 0.04 ) ^ { \mathrm { t } }$
C) $\mathrm { A } ( \mathrm { t } ) = \$ 90,000^{0.04} \mathrm { t }$
D) $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ^ { 1.04 \mathrm { t } }$

Accepted Answer

The formula for compound interest is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. In this case, $P = \$90,000$, $r = 0.04$ (4% as a decimal), and $t$ is the number of years. Therefore, the correct function is $A(t) = \$90,000(1.04)^t$.

Question 20

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year $2001 .$

A) About $\$ 500,000$
B) About $\$ 800,000$
C) About $\$ 900,000$
D) About $\$ 700,000$

Accepted Answer

The answer of Solve the problem.
-An accountant tabulated a firm's...

Quiz 12: Exponential Functions and Logarithmic Functions

Graph. - $f(x) =4^{3 x-2}$ $Graph. - f(x) =4^{3 x-2} A) B) C) D)$

Graph. - $f(x) =\left(\frac{1}{2}\right) ^{x}$ $Graph. - f(x) =\left(\frac{1}{2}\right) ^{x} A) B) C) D)$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$ .

Solve the problem. -The amount of particulate matter left in solution during a filtering process decreases by the equation $P ( n ) = 600 ( 0.5 ) ^ { 0.8 n }$ , where $n$ is the number of filtering steps. Find the amounts left for $n = 0$ and $n = 5$ . (Round to the nearest whole number.)

Graph. - $f(x) =4^{x-4}$ $Graph. - f(x) =4^{x-4} A) B) C) D)$

Graph. - $f(x) =\left(\frac{1}{4}\right) ^{x}+3$ $Graph. - f(x) =\left(\frac{1}{4}\right) ^{x}+3 A) B) C) D)$

Graph. - $f(x) =3^{-x}$ $Graph. - f(x) =3^{-x} A) B) C) D)$

Graph. - $f(x) = 3^{x}$ $Graph. - f(x) = 3^{x} A) B) C) D)$

Graph. - $x=\left(\frac{1}{2}\right) ^{y}$ $Graph. - x=\left(\frac{1}{2}\right) ^{y} A) B) C) D)$

Graph. - $x = 6 y$

Graph. - $f ( x ) = 3 ^ { x } - 2$ $Graph. - f ( x ) = 3 ^ { x } - 2 A) B) C) D)$

Solve the problem. -Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Quiz 12: Exponential Functions and Logarithmic Functions

Graph. - f(x) =43x−2f(x) =4^{3 x-2}f(x) =43x−2

Graph. - f(x) =(12) xf(x) =\left(\frac{1}{2}\right) ^{x}f(x) =(21​) x

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to B(x) =5300(2) XB ( x ) = 5300 ( 2 ) ^ { X }B(x) =5300(2) X , where xxx is time in days. Find the number of bacteria when x=0x = 0x=0 and x=5x = 5x=5 .

Graph. - f(x) =4x−4f(x) =4^{x-4}f(x) =4x−4

Graph. - f(x) =(14) x+3f(x) =\left(\frac{1}{4}\right) ^{x}+3f(x) =(41​) x+3

Graph. - f(x) =3−xf(x) =3^{-x}f(x) =3−x

Solve the problem. -The half-life of Antimony 111 is 2.92.92.9 hours. If the formula P(t) =(12) t/2.9\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { t / 2.9 }P(t) =(21​) t/2.9 gives the percent (as a decimal) remaining after time ttt (in hours) , sketch P versus ttt .

Graph. - f(x) =3xf(x) = 3^{x}f(x) =3x

Graph. - x=(12) yx=\left(\frac{1}{2}\right) ^{y}x=(21​) y

Graph. - x=6yx = 6 yx=6y

Graph. - f(x) =3x−2f ( x ) = 3 ^ { x } - 2f(x) =3x−2

Solve the problem. -Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Graph. - $f(x) =4^{3 x-2}$ $Graph. - f(x) =4^{3 x-2} A) B) C) D)$

Graph. - $f(x) =\left(\frac{1}{2}\right) ^{x}$ $Graph. - f(x) =\left(\frac{1}{2}\right) ^{x} A) B) C) D)$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$ .

Graph. - $f(x) =4^{x-4}$ $Graph. - f(x) =4^{x-4} A) B) C) D)$

Graph. - $f(x) =\left(\frac{1}{4}\right) ^{x}+3$ $Graph. - f(x) =\left(\frac{1}{4}\right) ^{x}+3 A) B) C) D)$

Graph. - $f(x) =3^{-x}$ $Graph. - f(x) =3^{-x} A) B) C) D)$

Graph. - $f(x) = 3^{x}$ $Graph. - f(x) = 3^{x} A) B) C) D)$

Graph. - $x=\left(\frac{1}{2}\right) ^{y}$ $Graph. - x=\left(\frac{1}{2}\right) ^{y} A) B) C) D)$

Graph. - $x = 6 y$

Graph. - $f ( x ) = 3 ^ { x } - 2$ $Graph. - f ( x ) = 3 ^ { x } - 2 A) B) C) D)$