Question 1

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 5 } x = - 3$

Accepted Answer

A)   -15 
B)  $\frac { 1 } { 125 }$ 
C)  2 
D)  $\frac { 1 } { 243 }$. 
A)   -15 
B)  $\frac { 1 } { 125 }$ 
C)  2 
D)  $\frac { 1 } { 243 }$.

Question 2

Give a definition for the following term: Exponential function .

Accepted Answer

A function defined by y @#LAT-DLM& x is

Question 3

A woman can sell her computer graphics company for $900,000 cash or for $100,000 plus $65,000 at the end of each year for 4 years. (a) Find the present value of the annuity that is offered if money is worth 7% compounded
Annually. (b) If she takes the $900,000, spends $100,000 of it, and invests the rest in a 4-year annuity at 7%
Compounded annually, what size annuity payment will she receive at the end of each year? (c) Which is better,
Taking the $100,000 and the annuity or taking the cash settlement?

Accepted Answer

A)  (a) $\$ 217,967.04$;
(b) $\$ 206,659.68$;
(c) $\$ 100,000$ plus the annuity has a smaller present value than $\$ 900,000$. She should take the cash settlemen 
B)  (a) $\$ 330,253.10$;
(b) $\$ 295,228.12$;
(c) $\$ 100,000$ plus the annuity has a larger present value than $\$ 900,000$. She should take $\$ 100,000$ plus the annuity. 
C)  (a) $\$ 297,227.79$;
(b) $\$ 265,705.31$;
(c) $\$ 100,000$ plus the annuity has a larger present value than $\$ 900,000$. She should take $\$ 100,000$ plus the annuity. 
D)  (a) $\$ 220,168.73$;
(b) $\$ 236,182.49$;
(c) $\$ 100,000$ plus the annuity has a smaller present value than $\$ 900,000$. She should take the cash settlemen 
A)  (a) $\$ 217,967.04$;
(b) $\$ 206,659.68$;
(c) $\$ 100,000$ plus the annuity has a smaller present value than $\$ 900,000$. She should take the cash settlemen 
B)  (a) $\$ 330,253.10$;
(b) $\$ 295,228.12$;
(c) $\$ 100,000$ plus the annuity has a larger present value than $\$ 900,000$. She should take $\$ 100,000$ plus the annuity. 
C)  (a) $\$ 297,227.79$;
(b) $\$ 265,705.31$;
(c) $\$ 100,000$ plus the annuity has a larger present value than $\$ 900,000$. She should take $\$ 100,000$ plus the annuity. 
D)  (a) $\$ 220,168.73$;
(b) $\$ 236,182.49$;
(c) $\$ 100,000$ plus the annuity has a smaller present value than $\$ 900,000$. She should take the cash settlemen

Question 4

Find the function value.
-Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$. Find $f ( - 2 )$.

Accepted Answer

A)  $\frac { 1 } { 36 }$ 
B)  $- \frac { 1 } { 36 }$ 
C)  36 
D)  $- 12$ 
A)  $\frac { 1 } { 36 }$ 
B)  $- \frac { 1 } { 36 }$ 
C)  36 
D)  $- 12$

Question 5

If an earthquake measured 6.1 on the Richter scale, what was the intensity of the earthquake? $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ Round to the nearest whole number.

Accepted Answer

A)  1,258,925 
B)  125,893 
C)  1,000,000 
D)  446 
A)  1,258,925 
B)  125,893 
C)  1,000,000 
D)  446

Question 6

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

Accepted Answer

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

Question 7

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
-$\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \log _ { 17 } 8$ 
B)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm { mn } - \frac { 1 } { 2 } \log _ { 17 } 8$ 
C)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 17 } 8$ 
D)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} \cdot \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } \div \frac { 1 } { 2 } \log _ { 17 } 8$ 
A)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \log _ { 17 } 8$ 
B)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm { mn } - \frac { 1 } { 2 } \log _ { 17 } 8$ 
C)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 17 } 8$ 
D)  $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} \cdot \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } \div \frac { 1 } { 2 } \log _ { 17 } 8$

Question 8

In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.8 e ^ { 0.0015 x }$. At the same time the population of East Goma in millions was modeled by $g ( x ) = 13.2 e ^ { 0.0164 x }$. In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.

Accepted Answer

A)  18 million 
B)  1 million 
C)  16 million 
D)  17 million 
A)  18 million 
B)  1 million 
C)  16 million 
D)  17 million

Question 9

Write in logarithmic form.
-$$9 ^ { 7 x } = y$$

Accepted Answer

A)  $\log _ { 9 } 7 x = y$ 
B)  $\log _ { y } 7 x = 9$ 
C)  $\log _ { 9 } y = 7 x$ 
D)  $\log _ { y } 9 = 7 x$ 
A)  $\log _ { 9 } 7 x = y$ 
B)  $\log _ { y } 7 x = 9$ 
C)  $\log _ { 9 } y = 7 x$ 
D)  $\log _ { y } 9 = 7 x$

Question 10

Provide an appropriate response.
-The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual
interest rate?

Accepted Answer

The answer of Provide an appropriate response.
-The function f \(f...

Question 11

Determine whether or not the given function is an exponential function.
-$y = e ^ { x ^ { 7 + 2 x } }$

Accepted Answer

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

Question 12

A company predicts that sales will increase rapidly after a new product is released, with the number of units sold weekly modeled by N $\mathrm { N } = 3000 ( 0.1 ) ^ { 0.5 ^ { t } }$ , where t represents the number of weeks after the product is released.
How many units per week were sold at the beginning of the campaign?

Accepted Answer

A)  360 units 
B)  3000 units 
C)  150 units 
D)  300 units 
A)  360 units 
B)  3000 units 
C)  150 units 
D)  300 units

Question 13

Determine if the function is a growth exponential or a decay exponential.
-$y = 9 e ^ { - 9 x }$

Accepted Answer

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

Question 14

The growth in the population of a certain rodent at a dump site fits the exponential function $A ( t ) = 102 e ^ { 0.018 t }$ where t is the number of years since 1965. Estimate the population in the year 2000.

Accepted Answer

A)  96 
B)  195 
C)  104 
D)  192 
A)  96 
B)  195 
C)  104 
D)  192

Question 15

Provide an appropriate response.
-Consider the logistic function $f ( x ) = \frac { c } { 1 + a e ^ { - b x } } , \text { where } b < 0 \text {. }$ 0. Is this function increasing or decreasing?

Accepted Answer

The functi

Question 16

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
-Lower levels of pH indicate a more acidic solution. If the pH of solution A is 4.2 and the pH of solution B is 6.9, how much more acidic is solution A than solution B?

Accepted Answer

A)  -0.0000630 times as acidic 
B)  0.00200 times as acidic 
C)  0.0000630 times as acidic 
D)  501.2 times as acidic 
A)  -0.0000630 times as acidic 
B)  0.00200 times as acidic 
C)  0.0000630 times as acidic 
D)  501.2 times as acidic

Question 17

Determine if the function is a growth exponential or a decay exponential.
-$y = 2 ^ { - 1.3 x }$

Accepted Answer

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

Question 18

Find the exponential function that models the data in the table below. Round the coefficients to the nearest hundredth. $\begin{array}{c|c|c|c|c|c}
\mathrm{x} & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{y} & 4.0 & 4.8 & 6.2 & 7.8 & 9.9
\end{array}$

Accepted Answer

A)  $f ( x ) = \frac { 3.95 } { 1 + 510.08 e ^ { - 2 x } }$ 
B)  $f ( x ) = 3.11 ( 1.26 ) ^ { x }$ 
C)  $f ( x ) = \frac { 3.95 } { 1 + 511.07 e ^ { - 2 x } } + 4.45$ 
D)  $f ( x ) = 3.33 ( 1.20 ) ^ { x }$ 
A)  $f ( x ) = \frac { 3.95 } { 1 + 510.08 e ^ { - 2 x } }$ 
B)  $f ( x ) = 3.11 ( 1.26 ) ^ { x }$ 
C)  $f ( x ) = \frac { 3.95 } { 1 + 511.07 e ^ { - 2 x } } + 4.45$ 
D)  $f ( x ) = 3.33 ( 1.20 ) ^ { x }$

Question 19

$4 ^ { ( 2 x + 1 ) } = 64$

Accepted Answer

A)  4 
B)  16 
C)  1 
D)   -1 
A)  4 
B)  16 
C)  1 
D)   -1

Question 20

The sales of a new product (in items per month) can be approximated by $S ( x ) = 325 + 200 \log ( 3 t + 1 )$ , where t represents the number of months after the item first becomes available. Find the number of items sold per
Month 3 months after the item first becomes available.

Accepted Answer

A)  4325 items per month 
B)  725 items per month 
C)  2325 items per month 
D)  525 items per month 
A)  4325 items per month 
B)  725 items per month 
C)  2325 items per month 
D)  525 items per month

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log _ { 5 } x = - 3$

Give a definition for the following term: Exponential function .

Find the function value. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( - 2 )$ .

If an earthquake measured 6.1 on the Richter scale, what was the intensity of the earthquake? $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ Round to the nearest whole number.

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

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }$

Write in logarithmic form. - $9 ^ { 7 x } = y$

Provide an appropriate response. -The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Determine whether or not the given function is an exponential function. - $y = e ^ { x ^ { 7 + 2 x } }$

Determine if the function is a growth exponential or a decay exponential. - $y = 9 e ^ { - 9 x }$

The growth in the population of a certain rodent at a dump site fits the exponential function $A ( t ) = 102 e ^ { 0.018 t }$ where t is the number of years since 1965. Estimate the population in the year 2000.

Provide an appropriate response. -Consider the logistic function $f ( x ) = \frac { c } { 1 + a e ^ { - b x } } , \text { where } b < 0 \text {. }$ 0. Is this function increasing or decreasing?

Determine if the function is a growth exponential or a decay exponential. - $y = 2 ^ { - 1.3 x }$

Find the exponential function that models the data in the table below. Round the coefficients to the nearest hundredth. 1 2 3 4 5 4.0 4.8 6.2 7.8 9.9

$4 ^ { ( 2 x + 1 ) } = 64$

The sales of a new product (in items per month) can be approximated by $S ( x ) = 325 + 200 \log ( 3 t + 1 )$ , where t represents the number of months after the item first becomes available. Find the number of items sold per Month 3 months after the item first becomes available.

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

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Exam 5: Exponential and Logarithmic Functions

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - log⁡5x=−3\log _ { 5 } x = - 3log5​x=−3

Give a definition for the following term: Exponential function .

Find the function value. -Let f(x)=(16)xf ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }f(x)=(61​)x . Find f(−2)f ( - 2 )f(−2) .

If an earthquake measured 6.1 on the Richter scale, what was the intensity of the earthquake? R=log⁡(II0)\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)R=log(I0​I​) Round to the nearest whole number.

Determine whether or not the given function is an exponential function. - y=x5y = x ^ { 5 }y=x5

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - log⁡17mn8\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }log17​8mn​​

Write in logarithmic form. - 97x=y9 ^ { 7 x } = y97x=y

Provide an appropriate response. -The function f f(x)=200(1+0.06/4)x−10.06/4f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }f(x)=2000.06/4(1+0.06/4)x−1​ describes the future value of a certain annuity. What is the annual interest rate?

Determine whether or not the given function is an exponential function. - y=ex7+2xy = e ^ { x ^ { 7 + 2 x } }y=ex7+2x

Determine if the function is a growth exponential or a decay exponential. - y=9e−9xy = 9 e ^ { - 9 x }y=9e−9x

The growth in the population of a certain rodent at a dump site fits the exponential function A(t)=102e0.018tA ( t ) = 102 e ^ { 0.018 t }A(t)=102e0.018t where t is the number of years since 1965. Estimate the population in the year 2000.

Provide an appropriate response. -Consider the logistic function f(x)=c1+ae−bx, where b<0. f ( x ) = \frac { c } { 1 + a e ^ { - b x } } , \text { where } b < 0 \text {. }f(x)=1+ae−bxc​, where b<0. 0. Is this function increasing or decreasing?

Determine if the function is a growth exponential or a decay exponential. - y=2−1.3xy = 2 ^ { - 1.3 x }y=2−1.3x

Find the exponential function that models the data in the table below. Round the coefficients to the nearest hundredth. 1 2 3 4 5 4.0 4.8 6.2 7.8 9.9

4(2x+1)=644 ^ { ( 2 x + 1 ) } = 644(2x+1)=64

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 a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log _ { 5 } x = - 3$

Find the function value. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( - 2 )$ .

If an earthquake measured 6.1 on the Richter scale, what was the intensity of the earthquake? $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ Round to the nearest whole number.

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

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }$

Write in logarithmic form. - $9 ^ { 7 x } = y$

Provide an appropriate response. -The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Determine whether or not the given function is an exponential function. - $y = e ^ { x ^ { 7 + 2 x } }$

Determine if the function is a growth exponential or a decay exponential. - $y = 9 e ^ { - 9 x }$

The growth in the population of a certain rodent at a dump site fits the exponential function $A ( t ) = 102 e ^ { 0.018 t }$ where t is the number of years since 1965. Estimate the population in the year 2000.

Provide an appropriate response. -Consider the logistic function $f ( x ) = \frac { c } { 1 + a e ^ { - b x } } , \text { where } b < 0 \text {. }$ 0. Is this function increasing or decreasing?

Determine if the function is a growth exponential or a decay exponential. - $y = 2 ^ { - 1.3 x }$

$4 ^ { ( 2 x + 1 ) } = 64$