Question 1

Solve the equation. $2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 40 )$

Accepted Answer

A)  $x = 14$ 
B)  $x = 10$ 
C)  none of these 
D)  $x = 8$ 
E)  $x = - 8$ 
A)  $x = 14$ 
B)  $x = 10$ 
C)  none of these 
D)  $x = 8$ 
E)  $x = - 8$

Question 2

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.08 \left( 1 - e ^ { - 0.1 t } \right)$. Find the initial concentration of the drug when $t = 0$.

Accepted Answer

A) 0.16 
B) 0.00 
C) 0.08 
D) 1.00 
E) 0.22
​ 
A) 0.16 
B) 0.00 
C) 0.08 
D) 1.00 
E) 0.22
​

Question 3

Use a calculator to find the value to four decimal places. $4 ^ { \sqrt { 3 } }$

Accepted Answer

A)  $6.0000$ 
B)  $6.9282$ 
C)  $2.3094$ 
D)  $11.0357$ 
E)  $\quad 9.0000$ 
A)  $6.0000$ 
B)  $6.9282$ 
C)  $2.3094$ 
D)  $11.0357$ 
E)  $\quad 9.0000$

Question 4

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 $\$ 6,000$ is invested each year in an annuity earning $10 \%$ annual interest, when will the account be worth $\$ 45,000$ ?

Accepted Answer

A)  $\quad - 3.0$ years 
B)  $\quad 2.8$ years 
C)  $\quad 5.9$ years 
D)  $\quad 13.5$ years 
E)  $\quad 7.5$ years 
A)  $\quad - 3.0$ years 
B)  $\quad 2.8$ years 
C)  $\quad 5.9$ years 
D)  $\quad 13.5$ years 
E)  $\quad 7.5$ years

Question 5

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.03 \left( 1 - e ^ { - 0.1 t } \right)$. Find the initial concentration of the drug when $t = 0$.

Accepted Answer

A)  $\quad 0.00$ 
B)  $\quad 0.06$ 
C)  $\quad 0.08$ 
D)  $\quad 1.00$ 
E)  $\quad 0.03$ 
A)  $\quad 0.00$ 
B)  $\quad 0.06$ 
C)  $\quad 0.08$ 
D)  $\quad 1.00$ 
E)  $\quad 0.03$

Question 6

Simplify the expression. $$5 ^ { \sqrt { 10 } } \cdot 5 ^ { \sqrt { 10 } }$$

Accepted Answer

A)  $\quad 25 \sqrt { 10 }$ 
B)  $\quad 5 ^ { \sqrt { 20 } }$ 
C)  $25 \sqrt { 20 }$ 
D)  $10 ^ { \sqrt { 5 } }$ 
E)  $\quad 10 \sqrt { 20 }$ 
A)  $\quad 25 \sqrt { 10 }$ 
B)  $\quad 5 ^ { \sqrt { 20 } }$ 
C)  $25 \sqrt { 20 }$ 
D)  $10 ^ { \sqrt { 5 } }$ 
E)  $\quad 10 \sqrt { 20 }$

Question 7

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

Accepted Answer

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

Question 8

A town's population grows at the rate of 4% per year.If this growth rate remains constant, how long will it take the population to double?

Accepted Answer

A)  $7.5$ years 
B)  $0.6$ years 
C)  $1.4$ years 
D)  $17.3$ years 
E)  $2.8$ years 
A)  $7.5$ years 
B)  $0.6$ years 
C)  $1.4$ years 
D)  $17.3$ years 
E)  $2.8$ years

Question 9

Find the db gain of an amplifier whose input voltage is 0.8 volts and whose output voltage is 20 volts.

Accepted Answer

A)  $\quad 1.4 \mathrm { db }$ 
B)  $\quad 27.96 \mathrm { db }$ 
C)  $\quad 64.38 \mathrm { db }$ 
D)  $\quad - 64.38 \mathrm { db }$ 
E)  $\quad 3 \mathrm { db }$ 
A)  $\quad 1.4 \mathrm { db }$ 
B)  $\quad 27.96 \mathrm { db }$ 
C)  $\quad 64.38 \mathrm { db }$ 
D)  $\quad - 64.38 \mathrm { db }$ 
E)  $\quad 3 \mathrm { db }$

Question 10

A cloth fragment is found in an ancient tomb.It contains 63% 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)  $\quad 10,600$ years 
B)  $\quad 8,200$ years 
C)  $\quad 9,000$ years 
D)  $\quad 8,600$ years 
E)  none of these 
A)  $\quad 10,600$ years 
B)  $\quad 8,200$ years 
C)  $\quad 9,000$ years 
D)  $\quad 8,600$ years 
E)  none of these

Question 11

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 9 hours?

Accepted Answer

A)  $\quad 0.9 \%$ 
B)  $\quad 15.4 \%$ 
C)  $\quad 6.7 \%$ 
D)  $\quad 5.4 \%$ 
E)  $\quad 0.1 \%$ 
A)  $\quad 0.9 \%$ 
B)  $\quad 15.4 \%$ 
C)  $\quad 6.7 \%$ 
D)  $\quad 5.4 \%$ 
E)  $\quad 0.1 \%$

Question 12

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 8 years?

Accepted Answer

A) 24,100 people 
B) 211,100 people 
C) 855,800 people 
D) 9,100 people 
E) 24,600 people 
A) 24,100 people 
B) 211,100 people 
C) 855,800 people 
D) 9,100 people 
E) 24,600 people

Question 13

Simplify the expression. $10 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }$

Accepted Answer

A)  $\quad 100 \sqrt { 20 }$ 
B)  $\quad 100 \sqrt { 10 }$ 
C)  $\quad 10 \sqrt { 20 }$ 
D)  $\quad 20 \sqrt { 20 }$ 
E)  $\quad 10 \sqrt { 10 }$ 
A)  $\quad 100 \sqrt { 20 }$ 
B)  $\quad 100 \sqrt { 10 }$ 
C)  $\quad 10 \sqrt { 20 }$ 
D)  $\quad 20 \sqrt { 20 }$ 
E)  $\quad 10 \sqrt { 10 }$

Question 14

True or False? $$\log _ { c } 6 = \log _ { 6 } c$$

Accepted Answer

A) True 
 B)False

Question 15

Simplify the expression. $5 ^ { \log 57 }$

Accepted Answer

A)  7 
B)  none of these 
C)  49 
D)  35 
E)  5 
A)  7 
B)  none of these 
C)  49 
D)  35 
E)  5

Question 16

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.08 \cdot 10 ^ { - 5 }$ gram-ions per liter.

Accepted Answer

A)  $\quad 4.9$ 
B)  $\quad 0.5$ 
C)  $\quad 4.96$ 
D)  5 
E)  $5.01$ 
A)  $\quad 4.9$ 
B)  $\quad 0.5$ 
C)  $\quad 4.96$ 
D)  5 
E)  $5.01$

Question 17

$$\text { Tell whether the statement } \log _ { 2 } 2 ^ { 5 } = 5 \left( 2 ^ { \log 2 ^ { 5 } } \right) \text { is true or false. }$$

Accepted Answer

A) True 
 B)False

Question 18

Solve the equation. $\log _ { 5 } x = \log _ { 5 } \frac { 1 } { x } + 2$

Accepted Answer

A)  $x = 5$ 
B)  $x = 13$ 
C)  $x = - 13$ 
D)  $x = - 2$ 
E)  $x = - 5$
F) $x = 2$ 
A)  $x = 5$ 
B)  $x = 13$ 
C)  $x = - 13$ 
D)  $x = - 2$ 
E)  $x = - 5$
F) $x = 2$

Question 19

An account now contains $9,100 and has been accumulating interest at a 14% annual rate, compounded continuously, for 12 years.Find the initial deposit.

Accepted Answer

A) $1,703.55 
B) $8,924.39 
C) $8,920.98 
D) $1,696.00 
E) $9,029.10 
A) $1,703.55 
B) $8,924.39 
C) $8,920.98 
D) $1,696.00 
E) $9,029.10

Question 20

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 $2,700 is invested each year in an annuity earning 15% annual interest, when will the account be
Worth $15,000?

Accepted Answer

A) 10.0 years 
B) 5.6 years 
C) 2.4 years 
D) -1.3 years 
E) 4.3 years 
A) 10.0 years 
B) 5.6 years 
C) 2.4 years 
D) -1.3 years 
E) 4.3 years

Solve the equation. $2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 40 )$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.08 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .

Use a calculator to find the value to four decimal places. $4 ^ { \sqrt { 3 } }$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.03 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .

Simplify the expression. $5 ^ { \sqrt { 10 } } \cdot 5 ^ { \sqrt { 10 } }$

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

A town's population grows at the rate of 4% per year.If this growth rate remains constant, how long will it take the population to double?

Find the db gain of an amplifier whose input voltage is 0.8 volts and whose output voltage is 20 volts.

A cloth fragment is found in an ancient tomb.It contains 63% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

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 9 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 8 years?

Simplify the expression. $10 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }$

True or False? $\log _ { c } 6 = \log _ { 6 } c$

Simplify the expression. $5 ^ { \log 57 }$

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.08 \cdot 10 ^ { - 5 }$ gram-ions per liter.

$\text { Tell whether the statement } \log _ { 2 } 2 ^ { 5 } = 5 \left( 2 ^ { \log 2 ^ { 5 } } \right) \text { is true or false. }$

Solve the equation. $\log _ { 5 } x = \log _ { 5 } \frac { 1 } { x } + 2$

An account now contains $9,100 and has been accumulating interest at a 14% annual rate, compounded continuously, for 12 years.Find the initial deposit.

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. 2log⁡2x=1+log⁡2(x+40)2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 40 )2log2​x=1+log2​(x+40)

The concentration xxx of a certain drug in an organ after ttt minutes is given by x=0.08(1−e−0.1t)x = 0.08 \left( 1 - e ^ { - 0.1 t } \right)x=0.08(1−e−0.1t) . Find the initial concentration of the drug when t=0t = 0t=0 .

Use a calculator to find the value to four decimal places. 434 ^ { \sqrt { 3 } }43​

The concentration xxx of a certain drug in an organ after ttt minutes is given by x=0.03(1−e−0.1t)x = 0.03 \left( 1 - e ^ { - 0.1 t } \right)x=0.03(1−e−0.1t) . Find the initial concentration of the drug when t=0t = 0t=0 .

Simplify the expression. 510⋅5105 ^ { \sqrt { 10 } } \cdot 5 ^ { \sqrt { 10 } }510​⋅510​

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

A town's population grows at the rate of 4% per year.If this growth rate remains constant, how long will it take the population to double?

Find the db gain of an amplifier whose input voltage is 0.8 volts and whose output voltage is 20 volts.

A cloth fragment is found in an ancient tomb.It contains 63% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

The percent PPP of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after t hours is given by P=e−0.3tP = e ^ { - 0.3 t }P=e−0.3t . What percent will remain in the bloodstream after 9 hours?

Simplify the expression. 1010⋅101010 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }1010​⋅1010​

True or False? log⁡c6=log⁡6c\log _ { c } 6 = \log _ { 6 } clogc​6=log6​c

Simplify the expression. 5log⁡575 ^ { \log 57 }5log57

Find the pH\mathrm { pH }pH of a solution with a hydrogen ion concentration of 1.08⋅10−51.08 \cdot 10 ^ { - 5 }1.08⋅10−5 gram-ions per liter.

Tell whether the statement log⁡225=5(2log⁡25) is true or false. \text { Tell whether the statement } \log _ { 2 } 2 ^ { 5 } = 5 \left( 2 ^ { \log 2 ^ { 5 } } \right) \text { is true or false. } Tell whether the statement log2​25=5(2log25) is true or false.

Solve the equation. log⁡5x=log⁡51x+2\log _ { 5 } x = \log _ { 5 } \frac { 1 } { x } + 2log5​x=log5​x1​+2

An account now contains $9,100 and has been accumulating interest at a 14% annual rate, compounded continuously, for 12 years.Find the initial deposit.

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. $2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 40 )$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.08 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .

Use a calculator to find the value to four decimal places. $4 ^ { \sqrt { 3 } }$

The concentration $x$ of a certain drug in an organ after $t$ minutes is given by $x = 0.03 \left( 1 - e ^ { - 0.1 t } \right)$ . Find the initial concentration of the drug when $t = 0$ .

Simplify the expression. $5 ^ { \sqrt { 10 } } \cdot 5 ^ { \sqrt { 10 } }$

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

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 9 hours?

Simplify the expression. $10 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }$

True or False? $\log _ { c } 6 = \log _ { 6 } c$

Simplify the expression. $5 ^ { \log 57 }$

Find the $\mathrm { pH }$ of a solution with a hydrogen ion concentration of $1.08 \cdot 10 ^ { - 5 }$ gram-ions per liter.

$\text { Tell whether the statement } \log _ { 2 } 2 ^ { 5 } = 5 \left( 2 ^ { \log 2 ^ { 5 } } \right) \text { is true or false. }$

Solve the equation. $\log _ { 5 } x = \log _ { 5 } \frac { 1 } { x } + 2$