Question 1

Graph the function.
-$f(x)=\log _{3}(x+4)$

Accepted Answer

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

Question 2

Find the function value.
-Let $f ( x ) = e ^ { 3 x }$. Find $f ( - 0.50 )$, rounded to four decimal places.

Accepted Answer

A)  $- 0.2231$ 
B)  $- 0.3502$ 
C)  $0.3502$ 
D)  $0.2231$ 
A)  $- 0.2231$ 
B)  $- 0.3502$ 
C)  $0.3502$ 
D)  $0.2231$

Question 3

A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  109 years 
B)  182 years 
C)  3 years 
D)  252 years 
A)  109 years 
B)  182 years 
C)  3 years 
D)  252 years

Question 4

Graph the function.
-$f(x)=4^{(x-1)}-1$

Accepted Answer

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

Question 5

Determine if the function is a growth exponential or a decay exponential.
-$y = 0.2 ^ { 7 x }$

Accepted Answer

A)  Growth 
B)  Decay 
A)  Growth 
B)  Decay

Question 6

You have money in an account at 6% interest, compounded weekly. To the nearest year, how long will it take for your money to double?

Accepted Answer

A)  9 years 
B)  16 years 
C)  7 years 
D)  12 years 
A)  9 years 
B)  16 years 
C)  7 years 
D)  12 years

Question 7

Tasha borrowed $13,000 to purchase a new car at an annual interest rate of 9%. She is to pay it back in equal monthly payments over a 5 year period. How much total interest will be paid over the period of the loan?
Round to the nearest dollar.

Accepted Answer

A)  $4145 
B)  $3192 
C)  $1457 
D)  $98 
A)  $4145 
B)  $3192 
C)  $1457 
D)  $98

Question 8

A sample of 200 grams of radioactive substance decays according to the function $\mathrm { A } ( \mathrm { t } ) = 200 \mathrm { e } ^ { - 0.031 \mathrm { t } }$ where t is the time in years. How much of the substance will be left in the sample after 40 years? Round your answer to the
Nearest whole gram.

Accepted Answer

A)  1 gram 
B)  2465 grams 
C)  58 grams 
D)  0 grams 
A)  1 gram 
B)  2465 grams 
C)  58 grams 
D)  0 grams

Question 9

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
-$\log _ { 8 } \frac { \sqrt { 13 } } { 7 }$

Accepted Answer

A)  $\log _ { 4 } \sqrt { 13 } - \log _ { 4 } 7$ 
B)  $\frac { 1 } { 2 } \log _ { 8 } 13 - \log _ { 8 } 7$ 
C)  $\log _ { 8 } 7 - \log _ { 8 } \sqrt { 13 }$ 
D)  $\log _ { 8 } \sqrt { 13 } + \log _ { 8 } 7$ 
A)  $\log _ { 4 } \sqrt { 13 } - \log _ { 4 } 7$ 
B)  $\frac { 1 } { 2 } \log _ { 8 } 13 - \log _ { 8 } 7$ 
C)  $\log _ { 8 } 7 - \log _ { 8 } \sqrt { 13 }$ 
D)  $\log _ { 8 } \sqrt { 13 } + \log _ { 8 } 7$

Question 10

At the end of t years, the future value of an investment of $7000 in an account that pays 7% APR compounded monthly is $S = 7000 \left( 1 + \frac { 0.07 } { 12 } \right) ^ { 12 t }$ dollars. Assuming no withdrawals or additional deposits, how long will it take
For the investment to reach $21,000? Round to three decimal places.

Accepted Answer

A)  23.610 years 
B)  15.740 years 
C)  12.592 years 
D)  18.888 years 
A)  23.610 years 
B)  15.740 years 
C)  12.592 years 
D)  18.888 years

Question 11

Find the exponential function that satisfies the given conditions.
-Initial population $= 30,848$, increasing at a rate of $3 \%$ per year

Accepted Answer

A)  $\mathrm { P } ( \mathrm { t } ) = 3 \cdot 30,848 ^ { \mathrm { t } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 3 ^ { \mathrm { t } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 1.03 ^ { \mathrm { t } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 0.03 \mathrm { t }$ 
A)  $\mathrm { P } ( \mathrm { t } ) = 3 \cdot 30,848 ^ { \mathrm { t } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 3 ^ { \mathrm { t } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 1.03 ^ { \mathrm { t } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = 30,848 \cdot 0.03 \mathrm { t }$

Question 12

Find the value of the logarithm without using a calculator.
-log (0.001)

Accepted Answer

A)  $- 2$ 
B)  0 
C)  $- 3$ 
D)  $- 1$ 
A)  $- 2$ 
B)  0 
C)  $- 3$ 
D)  $- 1$

Question 13

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. $\begin{array}{r|rrrr}
\mathrm{x} & 1 & 3 & 5 & 7 \
\hline \mathrm{y} & 1.23 & 2.51 & 4.05 & 6.92
\end{array}$

Accepted Answer

A)  $f ( x ) = ( 0.85 ) ( 1.14 ) ^ { x }$ 
B)  $f ( x ) = ( 1.14 ) ( 0.85 ) ^ { x }$ 
C)  $f ( x ) = ( 1.3
3 ) ( 0.98 ) ^ { x }$ 
D)  $f ( x ) = ( 0.98 ) ( 1.33 ) ^ { x }$ 
A)  $f ( x ) = ( 0.85 ) ( 1.14 ) ^ { x }$ 
B)  $f ( x ) = ( 1.14 ) ( 0.85 ) ^ { x }$ 
C)  $f ( x ) = ( 1.3
3 ) ( 0.98 ) ^ { x }$ 
D)  $f ( x ) = ( 0.98 ) ( 1.33 ) ^ { x }$

Question 14

Find the exponential function that models the data in the table below. $\begin{array}{l|l}
x & f(x) \
\hline-2 & -45 \
-1 & -27 \
0 & -16.2 \
1 & -9.72 \
2 & -5.832
\end{array}$

Accepted Answer

A)  $f ( x ) = - 45 \cdot 0.6 ^ { x }$ 
B)  $f ( x ) = - 16.2 \cdot 0.6 ^ { x }$ 
C)  $f ( x ) = 16.2 \cdot 1.4 ^ { x }$ 
D)  $f ( x ) = - 27 \cdot 1.6 ^ { x }$ 
A)  $f ( x ) = - 45 \cdot 0.6 ^ { x }$ 
B)  $f ( x ) = - 16.2 \cdot 0.6 ^ { x }$ 
C)  $f ( x ) = 16.2 \cdot 1.4 ^ { x }$ 
D)  $f ( x ) = - 27 \cdot 1.6 ^ { x }$

Question 15

Does it appear that a linear model or an exponential model is the better fit for the data given in the table below? Explain
your choice. $$\begin{array} { c | c } 
x & y \
\hline 2 & 3 \
\hline 4 & 5.5 \
\hline 6 & 7.8 \
\hline 8 & 10.3
\end{array}$$

Accepted Answer

Since the first differences ar

Question 16

Coyotes are one of the few species of North American animals with an expanding range. The future population of coyotes in a region of Mississippi can be modeled by the equation $P = 43 + 19 \ln ( 14 t + 1 )$ , where t is time in
Years. Use the equation to determine when the population will reach 140. Round to the nearest tenth when
Necessary.

Accepted Answer

A)  11.8 years 
B)  12 years 
C)  11.7 years 
D)  9101.9 years 
A)  11.8 years 
B)  12 years 
C)  11.7 years 
D)  9101.9 years

Question 17

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
-$\log _ { 2 } \frac { x ^ { 8 } y ^ { 7 } } { 5 }$

Accepted Answer

A)  $8 \log _ { 2 } x - 7 \log _ { 2 } y - \log _ { 2 } 5$ 
B)  $8 \log _ { 2 } x + 7 \log _ { 2 } y - \log _ { 2 } 5$ 
C)  $\left( 8 \log _ { 2 } x \right) \left( 7 \log _ { 2 } y \right) - \log _ { 2 } 5$ 
D)  $8 \log _ { 2 } x + 7 \log _ { 2 } y + \log _ { 2 } 5$ 
A)  $8 \log _ { 2 } x - 7 \log _ { 2 } y - \log _ { 2 } 5$ 
B)  $8 \log _ { 2 } x + 7 \log _ { 2 } y - \log _ { 2 } 5$ 
C)  $\left( 8 \log _ { 2 } x \right) \left( 7 \log _ { 2 } y \right) - \log _ { 2 } 5$ 
D)  $8 \log _ { 2 } x + 7 \log _ { 2 } y + \log _ { 2 } 5$

Question 18

Southwest Dry Cleaners believes that it will need new equipment in 9 years. The equipment will cost $26,000. What lump sum should be invested today at 12% compounded semiannually, to yield $26,000?

Accepted Answer

A)  $9108.94 
B)  $15,440.52 
C)  $19,593.79 
D)  $15,212.33 
A)  $9108.94 
B)  $15,440.52 
C)  $19,593.79 
D)  $15,212.33

Question 19

The pH of a solution is given by the formula $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right] , \text {where } \left[ \mathrm { H } ^ { + } \right]$ is the concentration of hydrogen ions in moles
per liter in the solution. Use this formula to
-Find the pH value of a sample of lake for which [ $\left[ \mathrm { H } ^ { + } \right] = 0.00000000305$ Round to the nearest tenth.

Accepted Answer

A)  7.3 
B)  8.5 
C)  10.1 
D)  6.4 
A)  7.3 
B)  8.5 
C)  10.1 
D)  6.4

Question 20

Find the value of the logarithm without using a calculator.
-$\ln e ^ { 9 }$

Accepted Answer

A)  $\frac { 1 } { 9 }$ 
B)  9 
C)  1 
D)  e $\ln 9$ 
A)  $\frac { 1 } { 9 }$ 
B)  9 
C)  1 
D)  e $\ln 9$

Graph the function. - $f(x)=\log _{3}(x+4)$ $Graph the function. - f(x)=\log _{3}(x+4)$

Find the function value. -Let $f ( x ) = e ^ { 3 x }$ . Find $f ( - 0.50 )$ , rounded to four decimal places.

A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.

Graph the function. - $f(x)=4^{(x-1)}-1$ $Graph the function. - f(x)=4^{(x-1)}-1$

Determine if the function is a growth exponential or a decay exponential. - $y = 0.2 ^ { 7 x }$

You have money in an account at 6% interest, compounded weekly. To the nearest year, how long will it take for your money to double?

Tasha borrowed $13,000 to purchase a new car at an annual interest rate of 9%. She is to pay it back in equal monthly payments over a 5 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 8 } \frac { \sqrt { 13 } } { 7 }$

Find the exponential function that satisfies the given conditions. -Initial population $= 30,848$ , increasing at a rate of $3 \%$ per year

Find the value of the logarithm without using a calculator. -log (0.001)

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. 1 3 5 7 1.23 2.51 4.05 6.92

Find the exponential function that models the data in the table below. x f(x) -2 -45 -1 -27 0 -16.2 1 -9.72 2 -5.832

Does it appear that a linear model or an exponential model is the better fit for the data given in the table below? Explain your choice. x y 2 3 4 5.5 6 7.8 8 10.3

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 2 } \frac { x ^ { 8 } y ^ { 7 } } { 5 }$

Southwest Dry Cleaners believes that it will need new equipment in 9 years. The equipment will cost $26,000. What lump sum should be invested today at 12% compounded semiannually, to yield $26,000?

Find the value of the logarithm without using a calculator. - $\ln e ^ { 9 }$

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)=log⁡3(x+4)f(x)=\log _{3}(x+4)f(x)=log3​(x+4)

Find the function value. -Let f(x)=e3xf ( x ) = e ^ { 3 x }f(x)=e3x . Find f(−0.50)f ( - 0.50 )f(−0.50) , rounded to four decimal places.

A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.

Graph the function. - f(x)=4(x−1)−1f(x)=4^{(x-1)}-1f(x)=4(x−1)−1

Determine if the function is a growth exponential or a decay exponential. - y=0.27xy = 0.2 ^ { 7 x }y=0.27x

You have money in an account at 6% interest, compounded weekly. To the nearest year, how long will it take for your money to double?

Tasha borrowed $13,000 to purchase a new car at an annual interest rate of 9%. She is to pay it back in equal monthly payments over a 5 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - log⁡8137\log _ { 8 } \frac { \sqrt { 13 } } { 7 }log8​713​​

Find the exponential function that satisfies the given conditions. -Initial population =30,848= 30,848=30,848 , increasing at a rate of 3%3 \%3% per year

Find the value of the logarithm without using a calculator. -log (0.001)

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. 1 3 5 7 1.23 2.51 4.05 6.92

Find the exponential function that models the data in the table below. x f(x) -2 -45 -1 -27 0 -16.2 1 -9.72 2 -5.832

Does it appear that a linear model or an exponential model is the better fit for the data given in the table below? Explain your choice. x y 2 3 4 5.5 6 7.8 8 10.3

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - log⁡2x8y75\log _ { 2 } \frac { x ^ { 8 } y ^ { 7 } } { 5 }log2​5x8y7​

Southwest Dry Cleaners believes that it will need new equipment in 9 years. The equipment will cost $26,000. What lump sum should be invested today at 12% compounded semiannually, to yield $26,000?

Find the value of the logarithm without using a calculator. - ln⁡e9\ln e ^ { 9 }lne9

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. - $f(x)=\log _{3}(x+4)$ $Graph the function. - f(x)=\log _{3}(x+4)$

Find the function value. -Let $f ( x ) = e ^ { 3 x }$ . Find $f ( - 0.50 )$ , rounded to four decimal places.

Graph the function. - $f(x)=4^{(x-1)}-1$ $Graph the function. - f(x)=4^{(x-1)}-1$

Determine if the function is a growth exponential or a decay exponential. - $y = 0.2 ^ { 7 x }$

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 8 } \frac { \sqrt { 13 } } { 7 }$

Find the exponential function that satisfies the given conditions. -Initial population $= 30,848$ , increasing at a rate of $3 \%$ per year

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 2 } \frac { x ^ { 8 } y ^ { 7 } } { 5 }$

Find the value of the logarithm without using a calculator. - $\ln e ^ { 9 }$