Question 1

Solve the equation. $$\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log x$$

Accepted Answer

A)  $\quad x = 32$ 
B)  $x = 34$ 
C)  $x = 4$ 
D)  $x = 36$ 
E)  none of these 
A)  $\quad x = 32$ 
B)  $x = 34$ 
C)  $x = 4$ 
D)  $x = 36$ 
E)  none of these

Question 2

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $100,000 if interest is paid
At a rate of 5% per year, compounded semiannually, for 8 years.

Accepted Answer

A) $46,319.35 
B) $67,362.49 
C) $67,683.94 
D) $53,390.82 
E) $5,408.79 
A) $46,319.35 
B) $67,362.49 
C) $67,683.94 
D) $53,390.82 
E) $5,408.79

Question 3

An account now contains $13,200 and has been accumulating interest at a 7% annual rate, compounded continuously, for 9 years.Find the initial deposit.

Accepted Answer

A) $13,185.47 
B) $7,030.21 
C) $7,023.91 
D) $13,134.59 
E) $13,135.73 
A) $13,185.47 
B) $7,030.21 
C) $7,023.91 
D) $13,134.59 
E) $13,135.73

Question 4

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated.

Accepted Answer

A)  $b = - \frac { 1 } { 5 }$ 
B)  $b = \frac { 3 } { 5 }$ 
C)  $b = \frac { 1 } { 5 }$ 
D)  $\quad b = 5$ 
E)  $b = - 5$ 
A)  $b = - \frac { 1 } { 5 }$ 
B)  $b = \frac { 3 } { 5 }$ 
C)  $b = \frac { 1 } { 5 }$ 
D)  $\quad b = 5$ 
E)  $b = - 5$

Question 5

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated.

Accepted Answer

A)  $b = \frac { 1 } { 5 }$ 
B)  $\quad b = - \frac { 1 } { 5 }$ 
C)  $b = - 5$ 
D)  $b = 5$ 
E)  $b = \frac { 3 } { 5 }$ 
A)  $b = \frac { 1 } { 5 }$ 
B)  $\quad b = - \frac { 1 } { 5 }$ 
C)  $b = - 5$ 
D)  $b = 5$ 
E)  $b = \frac { 3 } { 5 }$

Question 6

In one individual, the percent alcohol level $t$ minutes after two shots of whiskey is given by $P = 0.3 ( 1$ $e ^ { - 0.05 t }$ ). Find the blood alcohol level after 29 minutes.

Accepted Answer

A)  $\quad 0.118 \%$ 
B)  $\quad 0.230 \%$ 
C)  $\quad 0.285 \%$ 
D)  $\quad 0.070 \%$ 
E)  $\quad 0.370 \%$ 
A)  $\quad 0.118 \%$ 
B)  $\quad 0.230 \%$ 
C)  $\quad 0.285 \%$ 
D)  $\quad 0.070 \%$ 
E)  $\quad 0.370 \%$

Question 7

A Wisconsin lake is stocked with 10,500 bluegill. The population is expected to grow exponentially according to the model $P = P _ { 0 } 2 ^ { t / 2 }$. How many bluegill will be in the lake in 6 years?

Accepted Answer

A)  $\quad 42,000$ bluegill 
B)  $\quad 13,229$ bluegill 
C)  $\quad 63,000$ bluegill 
D)  $\quad 84,000$ bluegill 
E)  $\quad 126,000$ bluegill 
A)  $\quad 42,000$ bluegill 
B)  $\quad 13,229$ bluegill 
C)  $\quad 63,000$ bluegill 
D)  $\quad 84,000$ bluegill 
E)  $\quad 126,000$ bluegill

Question 8

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.93 \cdot 10 ^ { - 4 }$ gram-ions per liter.

Accepted Answer

A)  $\quad 3.7$ 
B)  $\quad 0.372$ 
C)  $\quad 3.72$ 
D)  $\quad 3.63$ 
E)  $\quad 3.67$ 
A)  $\quad 3.7$ 
B)  $\quad 0.372$ 
C)  $\quad 3.72$ 
D)  $\quad 3.63$ 
E)  $\quad 3.67$

Question 9

Use a calculator to find the value for to four decimal places.

Accepted Answer

A) −0.8416 
B) 0.8416 
C) 0.1583 
D) −0.1583 
E) −1.9379
​ 
A) −0.8416 
B) 0.8416 
C) 0.1583 
D) −0.1583 
E) −1.9379
​

Question 10

A town's population grows at the rate of 10% per year.If this growth rate remains constant, how long will it take the population to double?

Accepted Answer

A)  $ 4.6$ years 
B)  $2.3$ years 
C)  3 years 
D)  $6.9$ years 
E)  1 years 
A)  $ 4.6$ years 
B)  $2.3$ years 
C)  3 years 
D)  $6.9$ years 
E)  1 years

Question 11

A bacterial culture grows according to the formula $P = P _ { 0 } a ^ { t }$. If it takes 4 days for the culture to triple in size, how long will it take to double in size?

Accepted Answer

A)  $\quad - 0.9$ days 
B)  $\quad 5.0$ days 
C)  $\quad 2.1$ days 
D)  $\quad 0.4$ days 
E)  none of these 
A)  $\quad - 0.9$ days 
B)  $\quad 5.0$ days 
C)  $\quad 2.1$ days 
D)  $\quad 0.4$ days 
E)  none of these

Question 12

The percent $P$ of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after $t$ hours is given by $P = e ^ { - 0.3 t }$. What percent will remain in the bloodstream after 6 hours?

Accepted Answer

A) 0.2% 
B) 16.5% 
C) 28.7% 
D) 0.8% 
E) 3.6%
​ 
A) 0.2% 
B) 16.5% 
C) 28.7% 
D) 0.8% 
E) 3.6%
​

Question 13

In a city with a population of 1,200,000, there are currently 1000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula $$p = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }$$ how many people will be infected in 6 years?

Accepted Answer

A) 5,300 people 
B) 11,000 people 
C) 302,100 people 
D) 10,900 people 
E) 60,800 people 
A) 5,300 people 
B) 11,000 people 
C) 302,100 people 
D) 10,900 people 
E) 60,800 people

Question 14

A bacterial culture grows according to the formula $P = P _ { \mathrm { o } } a ^ { t }$. If it takes 4 days for the culture to triple in size, how long will it take to double in size?

Accepted Answer

A)  $\quad - 0.9$ days 
B)  $\quad 2.1$ days 
C)  $\quad 0.4$ days 
D)  $\quad 5.0$ days 
E)  none of these 
A)  $\quad - 0.9$ days 
B)  $\quad 2.1$ days 
C)  $\quad 0.4$ days 
D)  $\quad 5.0$ days 
E)  none of these

Question 15

Simplify the expression. $$2 ^ { \log _ { 2 } 4 }$$

Accepted Answer

A)  $\quad 8$ 
B)  16 
C)  $\quad 4$ 
D)  2 
E)  none of these 
A)  $\quad 8$ 
B)  16 
C)  $\quad 4$ 
D)  2 
E)  none of these

Question 16

Use a calculator to find the value to four decimal places.
$$6 ^ { \sqrt { 15 } }$$

Accepted Answer

A)  $\quad 760.0173$ 
B)  $\quad 1032.2071$ 
C)  $1.5492$ 
D)  $\quad 23.2379$ 
E)  $36.7423$ 
A)  $\quad 760.0173$ 
B)  $\quad 1032.2071$ 
C)  $1.5492$ 
D)  $\quad 23.2379$ 
E)  $36.7423$

Question 17

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.06 \left( 1 - e ^ { - 0.1 t } \right)$. Find the initial concentration of the drug when $t = 0$.

Accepted Answer

A) 0.06 
B) 1.00 
C) 0.00 
D) 0.12 
E) 0.16
​ 
A) 0.06 
B) 1.00 
C) 0.00 
D) 0.12 
E) 0.16
​

Question 18

A cloth fragment is found in an ancient tomb.It contains 71% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

Accepted Answer

A) 11,800 years 
B) none of these 
C) 13,500 years 
D) 11,500 years 
E) 11,700 years 
A) 11,800 years 
B) none of these 
C) 13,500 years 
D) 11,500 years 
E) 11,700 years

Question 19

If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where $$n = \frac { \log \left[ \frac { A r } { P } + 1 \right] } { \log ( 1 + r ) }$$
If $\$ 2,600$ is invested each year in an annuity earning $12 \%$ annual interest, when will the account be worth $\$ 30,000$ ?

Accepted Answer

A)  $\quad 11.5$ years 
B)  $\quad 2.8$ years 
C)  $\quad 2.9$ years 
D)  $\quad 7.7$ years 
E)  $\quad 17.7$ years 
A)  $\quad 11.5$ years 
B)  $\quad 2.8$ years 
C)  $\quad 2.9$ years 
D)  $\quad 7.7$ years 
E)  $\quad 17.7$ years

Question 20

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $1,000 if interest is paid at
A rate of 7% per year, compounded semiannually, for 9 years.

Accepted Answer

A) $7.23 
B) $452.80 
C) $299.25 
D) $538.36 
E) $543.93 
A) $7.23 
B) $452.80 
C) $299.25 
D) $538.36 
E) $543.93

Solve the equation. $\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log x$

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $100,000 if interest is paid At a rate of 5% per year, compounded semiannually, for 8 years.

An account now contains $13,200 and has been accumulating interest at a 7% annual rate, compounded continuously, for 9 years.Find the initial deposit.

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated. $Find the value of b that would cause the graph of y = b ^ { x } to look like the graph indicated.$

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated. $Find the value of b that would cause the graph of y = b ^ { x } to look like the graph indicated.$

In one individual, the percent alcohol level $t$ minutes after two shots of whiskey is given by $P = 0.3 ( 1$ $e ^ { - 0.05 t }$ ). Find the blood alcohol level after 29 minutes.

A Wisconsin lake is stocked with 10,500 bluegill. The population is expected to grow exponentially according to the model $P = P _ { 0 } 2 ^ { t / 2 }$ . How many bluegill will be in the lake in 6 years?

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.93 \cdot 10 ^ { - 4 }$ gram-ions per liter.

Use a calculator to find the value for to four decimal places.

A town's population grows at the rate of 10% per year.If this growth rate remains constant, how long will it take the population to double?

A bacterial culture grows according to the formula $P = P _ { 0 } a ^ { t }$ . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

The percent $P$ of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after $t$ hours is given by $P = e ^ { - 0.3 t }$ . What percent will remain in the bloodstream after 6 hours?

In a city with a population of 1,200,000, there are currently 1000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula $p = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }$ how many people will be infected in 6 years?

A bacterial culture grows according to the formula $P = P _ { \mathrm { o } } a ^ { t }$ . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

Simplify the expression. $2 ^ { \log _ { 2 } 4 }$

Use a calculator to find the value to four decimal places. $6 ^ { \sqrt { 15 } }$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.06 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .

A cloth fragment is found in an ancient tomb.It contains 71% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $1,000 if interest is paid at A rate of 7% per year, compounded semiannually, for 9 years.

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 5: Exponential and Logarithmic Functions

Solve the equation. log⁡(x−28)−log⁡8=log⁡(x−16)−log⁡x\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log xlog(x−28)−log8=log(x−16)−logx

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $100,000 if interest is paid At a rate of 5% per year, compounded semiannually, for 8 years.

An account now contains $13,200 and has been accumulating interest at a 7% annual rate, compounded continuously, for 9 years.Find the initial deposit.

Find the value of bbb that would cause the graph of y=bxy = b ^ { x }y=bx to look like the graph indicated.

Find the value of bbb that would cause the graph of y=bxy = b ^ { x }y=bx to look like the graph indicated.

In one individual, the percent alcohol level ttt minutes after two shots of whiskey is given by P=0.3(1P = 0.3 ( 1P=0.3(1 e−0.05te ^ { - 0.05 t }e−0.05t ). Find the blood alcohol level after 29 minutes.

A Wisconsin lake is stocked with 10,500 bluegill. The population is expected to grow exponentially according to the model P=P02t/2P = P _ { 0 } 2 ^ { t / 2 }P=P0​2t/2 . How many bluegill will be in the lake in 6 years?

Find the pH\mathrm { pH }pH of a solution with a hydrogen ion concentration of 1.93⋅10−41.93 \cdot 10 ^ { - 4 }1.93⋅10−4 gram-ions per liter.

Use a calculator to find the value for to four decimal places.

A town's population grows at the rate of 10% per year.If this growth rate remains constant, how long will it take the population to double?

A bacterial culture grows according to the formula P=P0atP = P _ { 0 } a ^ { t }P=P0​at . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

The percent PPP of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after ttt hours is given by P=e−0.3tP = e ^ { - 0.3 t }P=e−0.3t . What percent will remain in the bloodstream after 6 hours?

A bacterial culture grows according to the formula P=PoatP = P _ { \mathrm { o } } a ^ { t }P=Po​at . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

Simplify the expression. 2log⁡242 ^ { \log _ { 2 } 4 }2log2​4

Use a calculator to find the value to four decimal places. 6156 ^ { \sqrt { 15 } }615​

The concentration xxx of a certain drug in an organ after ttt minutes is given by x=0.06(1−e−0.1t)x = 0.06 \left( 1 - e ^ { - 0.1 t } \right)x=0.06(1−e−0.1t) . Find the initial concentration of the drug when t=0t = 0t=0 .

A cloth fragment is found in an ancient tomb.It contains 71% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $1,000 if interest is paid at A rate of 7% per year, compounded semiannually, for 9 years.

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Solve the equation. $\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log x$

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated. $Find the value of b that would cause the graph of y = b ^ { x } to look like the graph indicated.$

Find the value of $b$ that would cause the graph of $y = b ^ { x }$ to look like the graph indicated. $Find the value of b that would cause the graph of y = b ^ { x } to look like the graph indicated.$

In one individual, the percent alcohol level $t$ minutes after two shots of whiskey is given by $P = 0.3 ( 1$ $e ^ { - 0.05 t }$ ). Find the blood alcohol level after 29 minutes.

A Wisconsin lake is stocked with 10,500 bluegill. The population is expected to grow exponentially according to the model $P = P _ { 0 } 2 ^ { t / 2 }$ . How many bluegill will be in the lake in 6 years?

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.93 \cdot 10 ^ { - 4 }$ gram-ions per liter.

A bacterial culture grows according to the formula $P = P _ { 0 } a ^ { t }$ . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

The percent $P$ of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after $t$ hours is given by $P = e ^ { - 0.3 t }$ . What percent will remain in the bloodstream after 6 hours?

A bacterial culture grows according to the formula $P = P _ { \mathrm { o } } a ^ { t }$ . If it takes 4 days for the culture to triple in size, how long will it take to double in size?

Simplify the expression. $2 ^ { \log _ { 2 } 4 }$

Use a calculator to find the value to four decimal places. $6 ^ { \sqrt { 15 } }$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.06 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .