Question 1

Graph the function.
-$$f ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }$$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

$2 \mathrm { e } ^ { ( 3 x + 6 ) } = 10$ Round to three decimal places.

Accepted Answer

A)   1.333 
B)   -1.616 
C)   -1.464 
D)   2.536 
A)   1.333 
B)   -1.616 
C)   -1.464 
D)   2.536

Question 4

Find the inverse of the function.
-$$f ( x ) = e ^ { 7 x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 7 \ln x$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \ln \mathrm { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln \left( \frac { 1 } { 7 } \mathrm { x } \right)$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 7 \ln \mathrm { x }$ 
A)  $f ^ { - 1 } ( x ) = 7 \ln x$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \ln \mathrm { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln \left( \frac { 1 } { 7 } \mathrm { x } \right)$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 7 \ln \mathrm { x }$

Question 5

Use the properties of logarithms to evaluate the expression.
-$$\log _ { a } a ^ { 9 }$$

Accepted Answer

A)  $a ^ { 9 }$ 
B)  9 
C)  1 
D)  $9 \log _ { a } a$ 
A)  $a ^ { 9 }$ 
B)  9 
C)  1 
D)  $9 \log _ { a } a$

Question 6

-$$\text { Given } \log 2 = 0.3010 \text { and } \log 3 = 0.4771 \text {, evaluate } \log 12$$

Accepted Answer

A)  1.0791 
B)  0.2872 
C)  0.5677 
D)  1.2552 
A)  1.0791 
B)  0.2872 
C)  0.5677 
D)  1.2552

Question 7

Use the properties of logarithms to evaluate the expression.
-$6 ^ { \log _ { 6 } ( 2 x ) }$

Accepted Answer

A)  $6 ^ { 2 x }$ 
B)  1 
C)  6 
D)  $2 x$ 
A)  $6 ^ { 2 x }$ 
B)  1 
C)  6 
D)  $2 x$

Question 8

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-ln x-ln (x-4)=ln 4

Accepted Answer

A)  $\frac { 16 } { 3 }$ 
B)  $\frac { 4 \ln 4 } { \ln 4 - 1 }$ 
C)  0 
D)  no solution 
A)  $\frac { 16 } { 3 }$ 
B)  $\frac { 4 \ln 4 } { \ln 4 - 1 }$ 
C)  0 
D)  no solution

Question 9

The sales of a new model of notebook computer are approximated by $$S ( x ) = 5000 - 12,000 e ^ { - x / 8 }$$ , where x represents the number of months the computer has been on the market and S represents sales in thousands of
Dollars. In how many months will the sales reach $1,500,000?

Accepted Answer

A)  20 months 
B)  13 months 
C)  17 months 
D)  10 months 
A)  20 months 
B)  13 months 
C)  17 months 
D)  10 months

Question 10

Graph the function
-$f(x)=-2 \ln x$

Accepted Answer

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

Question 11

Write in logarithmic form.
-$$p = 9 ^ { t }$$

Accepted Answer

A)  $\log _ { t } 9 = \mathrm { p }$ 
B)  $\log _ { p } 9 = t$ 
C)  $\log { 9 } \mathrm { p } = \mathrm { t }$ 
D)  $\log _ { 9 } t = p$ 
A)  $\log _ { t } 9 = \mathrm { p }$ 
B)  $\log _ { p } 9 = t$ 
C)  $\log { 9 } \mathrm { p } = \mathrm { t }$ 
D)  $\log _ { 9 } t = p$

Question 12

Anwar invested $2500 at 4% compounded semiannually. In how many years will Anwar's investment have tripled? Round your answer to the nearest tenth of a year.

Accepted Answer

A)  3.5 years 
B)  4.2 years 
C)  27.5 years 
D)  27.7 years 
A)  3.5 years 
B)  4.2 years 
C)  27.5 years 
D)  27.7 years

Question 13

Graph the function.
-$$f ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }$$

Accepted Answer

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

Question 14

Graph the function
-$f(x)=\ln (x+5)$

Accepted Answer

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

Question 15

Find an exponential function to model the data below and use it to predict what income the company should expect in its seventh year of operation. Round to the nearest tenth when necessary. $$\begin{array} { c | c } 
\text { Years of Operation } & \begin{array} { c } 
\text { Annual Income } \
\text { (in millions) }
\end{array} \
\hline 1 & 0.3 \
2 & 0.7 \
3 & 1.2 \
4 & 1.9
\end{array}$$

Accepted Answer

A)  128 million 
B)  0.2 million 
C)  1.83 million 
D)  12.8 million 
A)  128 million 
B)  0.2 million 
C)  1.83 million 
D)  12.8 million

Question 16

A computer is purchased for $4100. Its value each year is about 75% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function $\mathrm { V } ( \mathrm { t } ) = 4100 ( 0.75 ) ^ { \mathrm { t } }$ Find the value of the computer after
2 years.

Accepted Answer

A)  $1297.27 
B)  $1729.69 
C)  $2306.25 
D)  $6150.00 
A)  $1297.27 
B)  $1729.69 
C)  $2306.25 
D)  $6150.00

Question 17

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

Accepted Answer

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

Question 18

Write the logarithmic equation in exponential form.
-$$\log _ { 3 } 9 = 2$$

Accepted Answer

A)  $3 ^ { 2 } = 9$ 
B)  $9 ^ { 2 } = 3$ 
C)  $3 ^ { 9 } = 2$ 
D)  $2 ^ { 3 } = 9$ 
A)  $3 ^ { 2 } = 9$ 
B)  $9 ^ { 2 } = 3$ 
C)  $3 ^ { 9 } = 2$ 
D)  $2 ^ { 3 } = 9$

Question 19

Gretta wants to retire in 13 years. At that time she wants to be able to withdraw $12,500 at the end of each 6 months for 14 years. Assume that money can be deposited at 6% per year compounded semiannually. What
Exact amount will Gretta need in 13 years?

Accepted Answer

A)  $239,855.63 
B)  $229,087.88 
C)  $234,551.37 
D)  $598,782.00 
A)  $239,855.63 
B)  $229,087.88 
C)  $234,551.37 
D)  $598,782.00

Question 20

The consumption of electricity can be modeled by C $C = A e ^ { r t }$ , where A is the current use, r is the rate at which the use is increasing, and t is the number of years. Suppose the consumption of electricity grows at 6.8% per year.
Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Accepted Answer

A)  0.16 year 
B)  44.12 years 
C)  1.62 years 
D)  16.16 years 
A)  0.16 year 
B)  44.12 years 
C)  1.62 years 
D)  16.16 years

Graph the function. - $f ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }$ $Graph the function. - f ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }$

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

$2 \mathrm { e } ^ { ( 3 x + 6 ) } = 10$ Round to three decimal places.

Find the inverse of the function. - $f ( x ) = e ^ { 7 x }$

Use the properties of logarithms to evaluate the expression. - $\log _ { a } a ^ { 9 }$

- $\text { Given } \log 2 = 0.3010 \text { and } \log 3 = 0.4771 \text {, evaluate } \log 12$

Use the properties of logarithms to evaluate the expression. - $6 ^ { \log _ { 6 } ( 2 x ) }$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -ln x-ln (x-4)=ln 4

The sales of a new model of notebook computer are approximated by $S ( x ) = 5000 - 12,000 e ^ { - x / 8 }$ , where x represents the number of months the computer has been on the market and S represents sales in thousands of Dollars. In how many months will the sales reach $1,500,000?

Graph the function - $f(x)=-2 \ln x$ $Graph the function - f(x)=-2 \ln x$

Write in logarithmic form. - $p = 9 ^ { t }$

Anwar invested $2500 at 4% compounded semiannually. In how many years will Anwar's investment have tripled? Round your answer to the nearest tenth of a year.

Graph the function. - $f ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }$ $Graph the function. - f ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }$

Graph the function - $f(x)=\ln (x+5)$ $Graph the function - f(x)=\ln (x+5)$

Find an exponential function to model the data below and use it to predict what income the company should expect in its seventh year of operation. Round to the nearest tenth when necessary. Years of Operation Annual Income (in millions) 1 0.3 2 0.7 3 1.2 4 1.9

A computer is purchased for $4100. Its value each year is about 75% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function $\mathrm { V } ( \mathrm { t } ) = 4100 ( 0.75 ) ^ { \mathrm { t } }$ Find the value of the computer after 2 years.

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

Write the logarithmic equation in exponential form. - $\log _ { 3 } 9 = 2$

Gretta wants to retire in 13 years. At that time she wants to be able to withdraw $12,500 at the end of each 6 months for 14 years. Assume that money can be deposited at 6% per year compounded semiannually. What Exact amount will Gretta need in 13 years?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 5: Exponential and Logarithmic Functions

Graph the function. - f(x)=4301+10e−0.2xf ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }f(x)=1+10e−0.2x430​

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

2e(3x+6)=102 \mathrm { e } ^ { ( 3 x + 6 ) } = 102e(3x+6)=10 Round to three decimal places.

Find the inverse of the function. - f(x)=e7xf ( x ) = e ^ { 7 x }f(x)=e7x

Use the properties of logarithms to evaluate the expression. - log⁡aa9\log _ { a } a ^ { 9 }loga​a9

- Given log⁡2=0.3010 and log⁡3=0.4771, evaluate log⁡12\text { Given } \log 2 = 0.3010 \text { and } \log 3 = 0.4771 \text {, evaluate } \log 12 Given log2=0.3010 and log3=0.4771, evaluate log12

Use the properties of logarithms to evaluate the expression. - 6log⁡6(2x)6 ^ { \log _ { 6 } ( 2 x ) }6log6​(2x)

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -ln x-ln (x-4)=ln 4

Graph the function - f(x)=−2ln⁡xf(x)=-2 \ln xf(x)=−2lnx

Write in logarithmic form. - p=9tp = 9 ^ { t }p=9t

Anwar invested $2500 at 4% compounded semiannually. In how many years will Anwar's investment have tripled? Round your answer to the nearest tenth of a year.

Graph the function. - f(x)=3000(0.002)0.5xf ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }f(x)=3000(0.002)0.5x

Graph the function - f(x)=ln⁡(x+5)f(x)=\ln (x+5)f(x)=ln(x+5)

Find an exponential function to model the data below and use it to predict what income the company should expect in its seventh year of operation. Round to the nearest tenth when necessary. Years of Operation Annual Income (in millions) 1 0.3 2 0.7 3 1.2 4 1.9

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

Write the logarithmic equation in exponential form. - log⁡39=2\log _ { 3 } 9 = 2log3​9=2

Gretta wants to retire in 13 years. At that time she wants to be able to withdraw $12,500 at the end of each 6 months for 14 years. Assume that money can be deposited at 6% per year compounded semiannually. What Exact amount will Gretta need in 13 years?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Graph the function. - $f ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }$ $Graph the function. - f ( x ) = \frac { 430 } { 1 + 10 e ^ { - 0.2 x } }$

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

$2 \mathrm { e } ^ { ( 3 x + 6 ) } = 10$ Round to three decimal places.

Find the inverse of the function. - $f ( x ) = e ^ { 7 x }$

Use the properties of logarithms to evaluate the expression. - $\log _ { a } a ^ { 9 }$

- $\text { Given } \log 2 = 0.3010 \text { and } \log 3 = 0.4771 \text {, evaluate } \log 12$

Use the properties of logarithms to evaluate the expression. - $6 ^ { \log _ { 6 } ( 2 x ) }$

Graph the function - $f(x)=-2 \ln x$ $Graph the function - f(x)=-2 \ln x$

Write in logarithmic form. - $p = 9 ^ { t }$

Graph the function. - $f ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }$ $Graph the function. - f ( x ) = 3000 ( 0.002 ) ^ { 0.5 ^ { x } }$

Graph the function - $f(x)=\ln (x+5)$ $Graph the function - f(x)=\ln (x+5)$

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

Write the logarithmic equation in exponential form. - $\log _ { 3 } 9 = 2$