Question 1

Solve for x.
-$$5 ^ { x } = \frac { 1 } { 25 }$$
A) $x = \frac { 1 } { 5 }$
B) $x = - 2$
C) $x = \frac { 1 } { 2 }$
D) $x = 2$

Accepted Answer

The equation $5^x = \frac{1}{25}$ can be rewritten as $5^x = 5^{-2}$, since $25 = 5^2$ and using the property that $\frac{1}{a^n} = a^{-n}$. Therefore, $x = -2$.

Question 2

Graph the function.
-$$f ( x ) = e ^ { 6 x }$$

A)
B)
C)
D)

Accepted Answer

A

Question 3

Graph the function.
-$(x)=4^{x-3}$

A)
B)
C)
D)

Accepted Answer

C

Question 4

Graph the function.
-$$f ( x ) = e ^ { x }$$

A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-\[f ( x ) =...

Question 5

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

A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-$f(x)=2^{x}$

A)
B)
C)
D)...

Question 6

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

A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-\[f ( x ) =...

Question 7

Solve for x.
-How much money will Lyle have in 6 years is he invests $\$ 9000$ at $17 \%$ annual rate of interest compounded quarterly? How much will he have if it is compounded monthly? Use the interest formula $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { n } t }$. Round the answers to the nearest cent.
A) $\$ 9964.30$ when compounded quarterly
$\$ 9965.73$ when compounded monthly
B) $\$ 24,438.13$ when compounded quarterly 
 $\$ 67,279.74$ when compounded monthly
C) $\$ 9964.30$ when compounded quarterly
 $\$ 24,780.75$ when compounded monthly 
D) $\$ 24,438.13$ when compounded quarterly
$\$ 24,780.75$ when compounded monthly

Accepted Answer

Using the formula $A = P\left(1 + \frac{r}{n}\right)^{nt}$, where $P = 9000$, $r = 0.17$, and $t = 6$, we calculate for both quarterly and monthly compounding. For quarterly compounding, $n = 4$, so $A = 9000\left(1 + \frac{0.17}{4}\right)^{4*6}$, which gives approximately \$24,438.13. For monthly compounding, $n = 12$, so $A = 9000\left(1 + \frac{0.17}{12}\right)^{12*6}$, which gives approximately \$24,780.75.

Question 8

Graph the function.
-$$f ( x ) = e ^ { x - 1 }$$

A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-\[f ( x ) =...

Question 9

Solve for x.
-$$4 - 3 x + 5 = \frac { 1 } { 256 }$$
A) $x = 128$
B) $x = \frac { 1 } { 64 }$
C) $x = 3$
D) $x = - 3$

Accepted Answer

The answer of Solve for x.
-\[4 - 3 x +...

Question 10

Solve for x.
-$$2 ^ { x } = 16$$
A) $x = 5$
B) $x = 8$
C) $x = 4$
D) $x = 3$

Accepted Answer

16 can be expressed as $2^4$, so $x = 4$.

Question 11

Solve for x.
-Mary is investing $\$ 8000$ at an annual rate of $5.4 \%$ compounded annually. How much money will Mary have after 6 years? Use the interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$. Round the answer to the nearest cent. 
A) $\$ 50,592.00$
B) $\$ 10,592.00$
C) $\$ 106,712.26$
D) $\$ 10,968.16$

Accepted Answer

Using the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$, where $P = 8000$, $r = 0.054$, $n = 1$, and $t = 6$, we calculate $A = 8000 \left( 1 + \frac {0.054}{1} \right)^{1 \times 6} = 8000 \times (1.054)^6 \approx 10968.16$.

Question 12

Solve for x.
-$$3 ^ { x } = 1$$
A) $x = 1$
B) $x = 0$
C) $x = \frac { 1 } { 8 }$
D) $\varnothing$

Accepted Answer

Any non-zero number raised to the power of 0 equals 1. Therefore, $3^0 = 1$, making $x = 0$ the correct answer.

Question 13

Solve for x.
-$$4 x - 1 = 1024$$
A) $x = 4$
B) $x = 2$
C) $x = 1$
D) $x = 3$

Accepted Answer

The answer of Solve for x.
-\[4 x - 1 =...

Question 14

Graph the function.
-
A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-
A)
B)
C)
D)...

Question 15

Solve for x.
-$$4 - 2 x + 10 = 256$$
A) $x = 5$
B) $x = 3$
C) $x = 64$
D) $x = - 3$

Accepted Answer

The answer of Solve for x.
-\[4 - 2 x +...

Question 16

Solve for x.
-$$2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$$
A) $x = 1$
B) $x = \frac { 1 } { 2 }$
C) $x = - 3$
D) $x = 3$

Accepted Answer

First, express $\frac{1}{4}$ as $2^{-2}$ to have the same base on both sides of the equation: $2^{3x+7} = 2^{-2}$. Then, set the exponents equal to each other because if $a^m = a^n$, then $m = n$. So, $3x + 7 = -2$. Solving for $x$, subtract 7 from both sides to get $3x = -9$, and then divide by 3 to find $x = -3$.

Question 17

Solve for x.
-$$4 ^ { - x } = \frac { 1 } { 16 }$$
A) $x = 2$
B) $x = \frac { 1 } { 2 }$
C) $x = - 2$
D) $x = \frac { 1 } { 4 }$

Accepted Answer

$$4^{-x} = \frac{1}{16}$$ can be rewritten as $$4^{-x} = 4^{-2}$$, indicating that $-x = -2$, thus $x = 2$.

Question 18

Graph the function.
-$$f ( x ) = 4 ^ { x } + 2$$

A)
B)
C)
D)

Accepted Answer

The answer of Graph the function.
-\[f ( x ) =...

Question 19

Solve for x.
-$$3 ^ { 2 x + 1 } = 27$$
A) $x = - 1$
B) $x = 9$
C) $x = 3$
D) $x = 1$

Accepted Answer

The equation can be rewritten as $3^{2x+1} = 3^3$, since $27 = 3^3$. By equating the exponents, $2x + 1 = 3$, solving for $x$ gives $x = 1$.

Question 20

Solve for x.
-The number of bacteria in a culture is given by $B ( t ) = 8000 \left( 2 ^ { t } \right)$, where $t$ is the time in hours. How many bacteria will grow in the culture in the first 8 hours?
A) $2,048,000$
B) 224,000
C) 128,000
D) 80,000

Accepted Answer

To find the number of bacteria after 8 hours, substitute $t = 8$ into the given formula: $B(8) = 8000 \times 2^8 = 8000 \times 256 = 2,048,000$.

Quiz 12: Logarithmic and Exponential Functions

Solve for x. - $5 ^ { x } = \frac { 1 } { 25 }$

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x } A) B) C) D)$

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

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

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

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

Graph the function. - $f ( x ) = e ^ { x - 1 }$ $Graph the function. - f ( x ) = e ^ { x - 1 } A) B) C) D)$

Solve for x. - $4 - 3 x + 5 = \frac { 1 } { 256 }$

Solve for x. - $2 ^ { x } = 16$

Solve for x. -Mary is investing $\$ 8000$ at an annual rate of $5.4 \%$ compounded annually. How much money will Mary have after 6 years? Use the interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ . Round the answer to the nearest cent.

Solve for x. - $3 ^ { x } = 1$

Solve for x. - $4 x - 1 = 1024$

Graph the function. -

Solve for x. - $4 - 2 x + 10 = 256$

Solve for x. - $2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$

Solve for x. - $4 ^ { - x } = \frac { 1 } { 16 }$

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

Solve for x. - $3 ^ { 2 x + 1 } = 27$

Solve for x. -The number of bacteria in a culture is given by $B ( t ) = 8000 \left( 2 ^ { t } \right)$ , where $t$ is the time in hours. How many bacteria will grow in the culture in the first 8 hours?

Quiz 12: Logarithmic and Exponential Functions

Solve for x. - 5x=1255 ^ { x } = \frac { 1 } { 25 }5x=251​

Graph the function. - f(x) =e6xf ( x ) = e ^ { 6 x }f(x) =e6x

Graph the function. - (x) =4x−3(x) =4^{x-3}(x) =4x−3

Graph the function. - f(x) =exf ( x ) = e ^ { x }f(x) =ex

Graph the function. - f(x) =2xf(x) =2^{x}f(x) =2x

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

Graph the function. - f(x) =ex−1f ( x ) = e ^ { x - 1 }f(x) =ex−1

Solve for x. - 4−3x+5=12564 - 3 x + 5 = \frac { 1 } { 256 }4−3x+5=2561​

Solve for x. - 2x=162 ^ { x } = 162x=16

Solve for x. -Mary is investing $8000\$ 8000$8000 at an annual rate of 5.4%5.4 \%5.4% compounded annually. How much money will Mary have after 6 years? Use the interest formula A=P(1+rn) ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​) nt . Round the answer to the nearest cent.

Solve for x. - 3x=13 ^ { x } = 13x=1

Solve for x. - 4x−1=10244 x - 1 = 10244x−1=1024

Graph the function. -

Solve for x. - 4−2x+10=2564 - 2 x + 10 = 2564−2x+10=256

Solve for x. - 23x+7=142 ^ { 3 x + 7 } = \frac { 1 } { 4 }23x+7=41​

Solve for x. - 4−x=1164 ^ { - x } = \frac { 1 } { 16 }4−x=161​

Graph the function. - f(x) =4x+2f ( x ) = 4 ^ { x } + 2f(x) =4x+2

Solve for x. - 32x+1=273 ^ { 2 x + 1 } = 2732x+1=27

Solve for x. -The number of bacteria in a culture is given by B(t) =8000(2t) B ( t ) = 8000 \left( 2 ^ { t } \right) B(t) =8000(2t) , where ttt is the time in hours. How many bacteria will grow in the culture in the first 8 hours?

Solve for x. - $5 ^ { x } = \frac { 1 } { 25 }$

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x } A) B) C) D)$

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

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

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

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

Graph the function. - $f ( x ) = e ^ { x - 1 }$ $Graph the function. - f ( x ) = e ^ { x - 1 } A) B) C) D)$

Solve for x. - $4 - 3 x + 5 = \frac { 1 } { 256 }$

Solve for x. - $2 ^ { x } = 16$

Solve for x. -Mary is investing $\$ 8000$ at an annual rate of $5.4 \%$ compounded annually. How much money will Mary have after 6 years? Use the interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ . Round the answer to the nearest cent.

Solve for x. - $3 ^ { x } = 1$

Solve for x. - $4 x - 1 = 1024$

Solve for x. - $4 - 2 x + 10 = 256$

Solve for x. - $2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$

Solve for x. - $4 ^ { - x } = \frac { 1 } { 16 }$

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

Solve for x. - $3 ^ { 2 x + 1 } = 27$

Solve for x. -The number of bacteria in a culture is given by $B ( t ) = 8000 \left( 2 ^ { t } \right)$ , where $t$ is the time in hours. How many bacteria will grow in the culture in the first 8 hours?