Question 1

Use the properties of logarithms to evaluate the expression.
-log  $10 ^ { - 12 }$

Accepted Answer

A)   log -12 
B)   -12 
C)  12 
D)   12 log 10 
A)   log -12 
B)   -12 
C)  12 
D)   12 log 10

Question 2

In order to purchase a home, a family borrows $45,000 at an annual interest rate of 9%, to be paid back over a 30 year period in equal monthly payments. What is their monthly payment?

Accepted Answer

A)  $362.08 
B)  $11.25 
C)  $337.50 
D)  $377.64 
A)  $362.08 
B)  $11.25 
C)  $337.50 
D)  $377.64

Question 3

Determine whether or not the given function is an exponential function.
-y $= 3 x - 5$

Accepted Answer

A)  exponential 
B)  not exponential 
A)  exponential 
B)  not exponential

Question 4

Find an exponential function to model the data below and use it to predict about how many widgets will be produced in 2019. Round to the nearest million widgets. $$\begin{array} { c | c } 
& \begin{array} { c } 
\text { Number of Widgets } \
\text { Years after 2010 }
\end{array} \
\hline 1 & 1.9 \
2 & 3.0 \
3 & 4.6 \
4 & 6.3 \
5 & 8.6
\end{array}$$

Accepted Answer

A)  41 million widgets 
B)  11 million widgets 
C)  60 million widgets 
D)  20 million widgets 
A)  41 million widgets 
B)  11 million widgets 
C)  60 million widgets 
D)  20 million widgets

Question 5

Find the value of the logarithm without using a calculator.
-$$\log _ { 7 } \frac { 1 } { 7 }$$

Accepted Answer

A)  7 
B)  0 
C)  -1 
D)  1 
A)  7 
B)  0 
C)  -1 
D)  1

Question 6

A company predicts that sales will increase rapidly after a new product is released, with the number of units sold weekly modeled by N $\mathrm { N } = 8000 ( 0.2 ) ^ { 0.5 ^ { t } }$ , where t represents the number of weeks after the product is released.
How many units per week were sold at the end of the first week of the campaign?

Accepted Answer

A)  2862 units 
B)  4293 units 
C)  5367 units 
D)  3578 units 
A)  2862 units 
B)  4293 units 
C)  5367 units 
D)  3578 units

Question 7

Use your graphing calculator to find how long it will take for $6600 invested at 5.85% per year compounded daily to triple in value. Find the answer to the nearest year.

Accepted Answer

A)  25,219 years 
B)  19 years 
C)  0 years 
D)  2,502,126 years 
A)  25,219 years 
B)  19 years 
C)  0 years 
D)  2,502,126 years

Question 8

Use the properties of logarithms to evaluate the expression.
-$e ^ { \ln x ^ { 41 } }$

Accepted Answer

A)  $\mathrm { e } ^ { \mathrm { x } ^ { 41 } }$ 
B)  $x ^ { 41 }$ 
C)  $x$ 
D)  $\ln x ^ { 41 }$ 
A)  $\mathrm { e } ^ { \mathrm { x } ^ { 41 } }$ 
B)  $x ^ { 41 }$ 
C)  $x$ 
D)  $\ln x ^ { 41 }$

Question 9

Several years ago, a large city undertook a major effort to encourage carpooling in order to reduce traffic congestion. The accompanying table shows the number of carpoolers, in thousands, from 2007 to  2012 .  Use regression to obtain a function  f(x)=a+b ln x  that models the data, where  x=1  corresponds to  2007, x=2  to 2008, and so on. Round the constants a and b to the nearest hundredth.
$\begin{array} { l | c | c | c | c | c | c } 
\text { Year } & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 \
\hline \text { Carpoolers } & 3.9 & 8.1 & 10.3 & 11.8 & 12.6 & 13.2
\end{array}$

Accepted Answer

A)   f(x)=4.22+5.25ln x 
B)   f(x)=4.33+5.17ln x 
C)   f(x)=4.29+5.14ln x 
D)   f(x)=4.40+5.32ln x 
A)   f(x)=4.22+5.25ln x 
B)   f(x)=4.33+5.17ln x 
C)   f(x)=4.29+5.14ln x 
D)   f(x)=4.40+5.32ln x

Question 10

The number of books in a small library increases according to the function B = 2700e0.05t, where t is measured in years. How many books will the library have after 4 years?

Accepted Answer

A)  3298 books 
B)  4279 books 
C)  4345 books 
D)  1887 books 
A)  3298 books 
B)  4279 books 
C)  4345 books 
D)  1887 books

Question 11

Find the amount of money in an account after 7 years if $2900 is deposited at 8% annual interest compounded semiannually.

Accepted Answer

A)  $5048.97 
B)  $5021.86 
C)  $5067.52 
D)  $4970.09 
A)  $5048.97 
B)  $5021.86 
C)  $5067.52 
D)  $4970.09

Question 12

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary.
-$$130 \mathrm { e } ^ { \mathrm { rt } } \text { for } \mathrm { t } = 6 \text { and } \mathrm { r } = 2 \%$$

Accepted Answer

A)  $2611.12 
B)  $181.43 
C)  $353.38 
D)  $146.57 
A)  $2611.12 
B)  $181.43 
C)  $353.38 
D)  $146.57

Question 13

$2500 is invested at 6% compounded quarterly. In how many years will the account have grown to $6000? Round your answer to the nearest tenth of a year.

Accepted Answer

A)  1.2 years 
B)  18.5 years 
C)  15.0 years 
D)  14.7 years 
A)  1.2 years 
B)  18.5 years 
C)  15.0 years 
D)  14.7 years

Question 14

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.7 ln x+6.4  compute the wind speed  x  meters above the ground. What is the wind speed 9 meters above the ground? Round your result to the nearest hundredth.

Accepted Answer

A)   -2.66  meters per second 
B)   10.14  meters per second 
C)   9.56  meters per second 
D)   8.60  meters per second 
A)   -2.66  meters per second 
B)   10.14  meters per second 
C)   9.56  meters per second 
D)   8.60  meters per second

Question 15

Find the inverse of the function.
-$$f ( x ) = 5 ^ { x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \log _ { 5 } x$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \ln ( 5 x )$ 
D)  $f ^ { - 1 } ( x ) = \log _ { x } 5$ 
A)  $f ^ { - 1 } ( x ) = \log _ { 5 } x$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \ln ( 5 x )$ 
D)  $f ^ { - 1 } ( x ) = \log _ { x } 5$

Question 16

Estimate the $y$-value associated with $x = 35$ as predicted by the natural logarithmic regression equation for the following data. Round to the nearest hundredth.
$$\begin{array} { c | c } 
\mathrm { x } & \mathrm { y } \
\hline 10 & 1.51 \
20 & 2.88 \
30 & 3.71 \
40 & 4.36
\end{array}$$

Accepted Answer

A)  3.75 
B)  3.55 
C)  4.25 
D)  4.05 
A)  3.75 
B)  3.55 
C)  4.25 
D)  4.05

Question 17

If $1000 is invested at the end of each year in an annuity that pays 8%, compounded annually, the number of years it takes for the future value to amount to $22,000 is given by $t = \log 1.08^{177}$ Use the change of base
Formula to find the number of years until the future value is $22,000, to the nearest tenth of a year.

Accepted Answer

A)  67.3 years 
B)  72.3 years 
C)  65.0 years 
D)  74.4 years 
A)  67.3 years 
B)  72.3 years 
C)  65.0 years 
D)  74.4 years

Question 18

Evaluate the logarithm, if possible. Round the answer to four decimal places.
-ln 0.994

Accepted Answer

A)  0.0060 
B)  0.0026 
C)  -0.0026 
D)  -0.0060 
A)  0.0060 
B)  0.0026 
C)  -0.0026 
D)  -0.0060

Question 19

Provide an appropriate response.
-Explain why f(x) $f ( x ) = 2 ^ { x } \text { is an exponential function but } f ( x ) = x ^ { 2 }$ is not.

Accepted Answer

@#LAT-DLM& is an exponential function be

Question 20

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the functi $\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - 0.189 t }$ , where t is the time in years? Round your answer to the nearest
Hundredth year.

Accepted Answer

A)  3.67 years 
B)  34.27 years 
C)  122.85 years 
D)  37.94 years 
A)  3.67 years 
B)  34.27 years 
C)  122.85 years 
D)  37.94 years

Use the properties of logarithms to evaluate the expression. -log $10 ^ { - 12 }$

In order to purchase a home, a family borrows $45,000 at an annual interest rate of 9%, to be paid back over a 30 year period in equal monthly payments. What is their monthly payment?

Determine whether or not the given function is an exponential function. -y $= 3 x - 5$

Find an exponential function to model the data below and use it to predict about how many widgets will be produced in 2019. Round to the nearest million widgets. Number of Widgets Years after 2010 1 1.9 2 3.0 3 4.6 4 6.3 5 8.6

Find the value of the logarithm without using a calculator. - $\log _ { 7 } \frac { 1 } { 7 }$

Use your graphing calculator to find how long it will take for $6600 invested at 5.85% per year compounded daily to triple in value. Find the answer to the nearest year.

Use the properties of logarithms to evaluate the expression. - $e ^ { \ln x ^ { 41 } }$

The number of books in a small library increases according to the function B = 2700e0.05t, where t is measured in years. How many books will the library have after 4 years?

Find the amount of money in an account after 7 years if $2900 is deposited at 8% annual interest compounded semiannually.

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - $130 \mathrm { e } ^ { \mathrm { rt } } \text { for } \mathrm { t } = 6 \text { and } \mathrm { r } = 2 \%$

$2500 is invested at 6% compounded quarterly. In how many years will the account have grown to $6000? Round your answer to the nearest tenth of a year.

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.7 ln x+6.4 compute the wind speed x meters above the ground. What is the wind speed 9 meters above the ground? Round your result to the nearest hundredth.

Find the inverse of the function. - $f ( x ) = 5 ^ { x }$

Estimate the $y$ -value associated with $x = 35$ as predicted by the natural logarithmic regression equation for the following data. Round to the nearest hundredth. 10 1.51 20 2.88 30 3.71 40 4.36

Evaluate the logarithm, if possible. Round the answer to four decimal places. -ln 0.994

Provide an appropriate response. -Explain why f(x) $f ( x ) = 2 ^ { x } \text { is an exponential function but } f ( x ) = x ^ { 2 }$ is not.

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the functi $\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - 0.189 t }$ , where t is the time in years? Round your answer to the nearest Hundredth year.

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

Use the properties of logarithms to evaluate the expression. -log 10−1210 ^ { - 12 }10−12

In order to purchase a home, a family borrows $45,000 at an annual interest rate of 9%, to be paid back over a 30 year period in equal monthly payments. What is their monthly payment?

Determine whether or not the given function is an exponential function. -y =3x−5= 3 x - 5=3x−5

Find an exponential function to model the data below and use it to predict about how many widgets will be produced in 2019. Round to the nearest million widgets. Number of Widgets Years after 2010 1 1.9 2 3.0 3 4.6 4 6.3 5 8.6

Find the value of the logarithm without using a calculator. - log⁡717\log _ { 7 } \frac { 1 } { 7 }log7​71​

Use your graphing calculator to find how long it will take for $6600 invested at 5.85% per year compounded daily to triple in value. Find the answer to the nearest year.

Use the properties of logarithms to evaluate the expression. - eln⁡x41e ^ { \ln x ^ { 41 } }elnx41

The number of books in a small library increases according to the function B = 2700e0.05t, where t is measured in years. How many books will the library have after 4 years?

Find the amount of money in an account after 7 years if $2900 is deposited at 8% annual interest compounded semiannually.

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - 130ert for t=6 and r=2%130 \mathrm { e } ^ { \mathrm { rt } } \text { for } \mathrm { t } = 6 \text { and } \mathrm { r } = 2 \%130ert for t=6 and r=2%

$2500 is invested at 6% compounded quarterly. In how many years will the account have grown to $6000? Round your answer to the nearest tenth of a year.

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.7 ln x+6.4 compute the wind speed x meters above the ground. What is the wind speed 9 meters above the ground? Round your result to the nearest hundredth.

Find the inverse of the function. - f(x)=5xf ( x ) = 5 ^ { x }f(x)=5x

Estimate the yyy -value associated with x=35x = 35x=35 as predicted by the natural logarithmic regression equation for the following data. Round to the nearest hundredth. 10 1.51 20 2.88 30 3.71 40 4.36

Evaluate the logarithm, if possible. Round the answer to four decimal places. -ln 0.994

Provide an appropriate response. -Explain why f(x) f(x)=2x is an exponential function but f(x)=x2f ( x ) = 2 ^ { x } \text { is an exponential function but } f ( x ) = x ^ { 2 }f(x)=2x is an exponential function but f(x)=x2 is not.

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

Use the properties of logarithms to evaluate the expression. -log $10 ^ { - 12 }$

Determine whether or not the given function is an exponential function. -y $= 3 x - 5$

Find the value of the logarithm without using a calculator. - $\log _ { 7 } \frac { 1 } { 7 }$

Use the properties of logarithms to evaluate the expression. - $e ^ { \ln x ^ { 41 } }$

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - $130 \mathrm { e } ^ { \mathrm { rt } } \text { for } \mathrm { t } = 6 \text { and } \mathrm { r } = 2 \%$

Find the inverse of the function. - $f ( x ) = 5 ^ { x }$

Estimate the $y$ -value associated with $x = 35$ as predicted by the natural logarithmic regression equation for the following data. Round to the nearest hundredth. 10 1.51 20 2.88 30 3.71 40 4.36

Provide an appropriate response. -Explain why f(x) $f ( x ) = 2 ^ { x } \text { is an exponential function but } f ( x ) = x ^ { 2 }$ is not.