Question 1

Evaluate the function as indicated. Round to three decimal places if necessary. $\begin{array} { c } 
10,000 ( 1.01 ) ^ { 3 t } \
t = 3
\end{array}$

Accepted Answer

A) 10,303.010 
B) 10,936.853 
C) 91,999.387 
D) 4702.847 
E) 90,900.000 
A) 10,303.010 
B) 10,936.853 
C) 91,999.387 
D) 4702.847 
E) 90,900.000

Question 2

Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000 dollars when invested at rate r=9% for 40 years, compounded 4 times per year. Round the answer to two decimal places.

Accepted Answer

A) $173,611.11 
B) $14,218.75 
C) $1,026,614.38 
D) $147,569.44 
E) $71,090.14 
A) $173,611.11 
B) $14,218.75 
C) $1,026,614.38 
D) $147,569.44 
E) $71,090.14

Question 3

Evaluate the function as indicated. Round your answer to three decimal places. $\begin{aligned}
G ( x ) & = 1.5 ^ { - x } \
x & = 1
\end{aligned}$

Accepted Answer

A) 0.500 
B) 0.667 
C) 2.500 
D) -0.667 
E) -1.500 
A) 0.500 
B) 0.667 
C) 2.500 
D) -0.667 
E) -1.500

Question 4

A deposit of $10,000 is placed in a savings account for 4 years. The interest for the account is compounded continuously. At the end of 4 years, the balance in the account is $12,068.34. What is the annual interest rate for this account. Round your answer to one decimal places.

Accepted Answer

A) 75.2% 
B) 2.0% 
C) 5.2% 
D) 4.7% 
E) none of these 
A) 75.2% 
B) 2.0% 
C) 5.2% 
D) 4.7% 
E) none of these

Question 5

Use a calculator to evaluate $\log _ { 3 } 215$ by means of the change-of-base formula. Round your answer to four decimal places.

Accepted Answer

A) 2.1231 
B) 11.2563 
C) 4.272 
D) 0.2046 
E) 4.8886 
A) 2.1231 
B) 11.2563 
C) 4.272 
D) 0.2046 
E) 4.8886

Question 6

Evaluate the function as indicated. Round your answer to three decimal places. $\begin{aligned}
G ( x ) & = 1.7 ^ { - x } \
x & = \sqrt { 3 }
\end{aligned}$

Accepted Answer

A) 0.399 
B) -2.944 
C) -0.032 
D) 2.507 
E) not a real number 
A) 0.399 
B) -2.944 
C) -0.032 
D) 2.507 
E) not a real number

Question 7

Find the domain of $g \circ f$ where $f ( x ) = \sqrt { x - 2 }$ and $g ( x ) = x + 6$ .

Accepted Answer

A)  $[ 2 , \infty )$ 
B)  $[ 4 , \infty )$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 6 , \infty )$ 
E)  $[ 0 , \infty )$ 
A)  $[ 2 , \infty )$ 
B)  $[ 4 , \infty )$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 6 , \infty )$ 
E)  $[ 0 , \infty )$

Question 8

Find $( f \circ g ) ( x )$ where $f ( x ) = 2 x + 6$ and $g ( x ) = x ^ { 2 } - 2$ .

Accepted Answer

A)  $2 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12$ 
B)  $2 x ^ { 2 } + 2$ 
C)  $4 x ^ { 2 } + 24 x + 34$ 
D)  $4 x ^ { 2 } + 4$ 
E)  $2 x ^ { 2 } + 4$ 
A)  $2 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12$ 
B)  $2 x ^ { 2 } + 2$ 
C)  $4 x ^ { 2 } + 24 x + 34$ 
D)  $4 x ^ { 2 } + 4$ 
E)  $2 x ^ { 2 } + 4$

Question 9

Find the domain of $g \circ f$ where $f ( x ) = \frac { x } { x - 5 }$ and $g ( x ) = \sqrt { x }$ .

Accepted Answer

A)  $[ 0,5 ) \cup ( 5 , \infty )$ 
B)  $( 25 , \infty )$ 
C)  $( - \infty , 0 ] \cup ( 5 , \infty )$ 
D)  $[ 0,25 ) \cup ( 25 , \infty )$ 
E)  $( - \infty , 25 ) \cup ( 25 , \infty )$ 
A)  $[ 0,5 ) \cup ( 5 , \infty )$ 
B)  $( 25 , \infty )$ 
C)  $( - \infty , 0 ] \cup ( 5 , \infty )$ 
D)  $[ 0,25 ) \cup ( 25 , \infty )$ 
E)  $( - \infty , 25 ) \cup ( 25 , \infty )$

Question 10

Solve the exponential equation $100,000 = 50,000 e ^ { 25 r }$ for r to determine the interest rate required for an investment of $50,000 to double in value when compounded continuously for 25 years. Round your answer to one decimal place.

Accepted Answer

A) 2.5% 
B) 3.9% 
C) 6.4% 
D) 2.8% 
E) none of these 
A) 2.5% 
B) 3.9% 
C) 6.4% 
D) 2.8% 
E) none of these

Question 11

An investment of $2500 is made in an account that compounds interest quarterly. After years 30 the balance in the account is $26132.78. To the nearest tenth of a percent, what is the annual interest rate for this account?

Accepted Answer

A)  $2.0 \%$ 
B)  $0.5 \%$ 
C)  $31.5 \%$ 
D)  $7.9 \%$ 
E)  $2.6 \%$ 
A)  $2.0 \%$ 
B)  $0.5 \%$ 
C)  $31.5 \%$ 
D)  $7.9 \%$ 
E)  $2.6 \%$

Question 12

Find the domain and vertical asymptote of $g ( x ) = - \log _ { 5 } ( x + 1 )$ .

Accepted Answer

A) Domain: $( - \infty , \infty )$ Asymptote: $x = - 1$ 
B) Domain: $( - 1 , \infty )$ Asymptote: $x = - 1$ 
C) Domain: $( - 1 , \infty )$ Asymptote: y -axis 
D) Domain: $( 0 , \infty )$ Asymptote: y -axis 
E) Domain: $( 0 , \infty )$ Asymptote: $x = - 1$ 
A) Domain: $( - \infty , \infty )$ Asymptote: $x = - 1$ 
B) Domain: $( - 1 , \infty )$ Asymptote: $x = - 1$ 
C) Domain: $( - 1 , \infty )$ Asymptote: y -axis 
D) Domain: $( 0 , \infty )$ Asymptote: y -axis 
E) Domain: $( 0 , \infty )$ Asymptote: $x = - 1$

Question 13

Solve the logarithmic equation. Round your answer to two decimal places. $$\log _ { 6 } ( x - 1 ) - \log _ { 6 } 3 = 7$$

Accepted Answer

A)  $x = 279,937.61$ 
B)  $x = 456,556.95$ 
C)  $x = 279,940.00$ 
D)  $x = 839,809.00$ 
E)  $x = 93,313.00$ 
A)  $x = 279,937.61$ 
B)  $x = 456,556.95$ 
C)  $x = 279,940.00$ 
D)  $x = 839,809.00$ 
E)  $x = 93,313.00$

Question 14

Find the domain and vertical asymptote of $f ( x ) = - \log _ { 2 } x + 3$ .

Accepted Answer

A) Domain: $( 0 , \infty )$ Asymptote: y -axis 
B) Domain: $( 0 , \infty )$ Asymptote: x=3 
C) Domain: $( 3 , \infty )$ Asymptote: $x = 8.00$ 
D) Domain: $( - \infty , \infty )$ Asymptote: y -axis 
E) Domain: $( 3 , \infty )$ Asymptote: y -axis 
A) Domain: $( 0 , \infty )$ Asymptote: y -axis 
B) Domain: $( 0 , \infty )$ Asymptote: x=3 
C) Domain: $( 3 , \infty )$ Asymptote: $x = 8.00$ 
D) Domain: $( - \infty , \infty )$ Asymptote: y -axis 
E) Domain: $( 3 , \infty )$ Asymptote: y -axis

Question 15

Evaluate the function as indicated. Round to three decimal places if necessary. 
$\begin{array}{ c}
10,000 ( 1.07 ) ^ { 4 t } \
 t = 1
\end{array}$

Accepted Answer

A) 13,107.960 
B) 1310.796 
C) 10,700.000 
D) 42,800.000 
E) 44,076.205 
A) 13,107.960 
B) 1310.796 
C) 10,700.000 
D) 42,800.000 
E) 44,076.205

Question 16

Evaluate the logarithm. $\log _ { 6 } ( - 6 )$

Accepted Answer

A) 0 
B)  $\frac { 1 } { 6 }$ 
C)  -1 
D)  $e^ { - 1 }$ 
E)  $\log _ { 6 } ( - 6 )$ is undefined. 
A) 0 
B)  $\frac { 1 } { 6 }$ 
C)  -1 
D)  $e^ { - 1 }$ 
E)  $\log _ { 6 } ( - 6 )$ is undefined.

Question 17

Solve the equation. Do not use a calculator. $$\log _ { 6 } 8 x = \log _ { 6 } 48$$

Accepted Answer

A)  $x = 48$ 
B)  $x = 6$ 
C)  $x = 1$ 
D)  $x = 8$ 
E)  $x = 7$ 
A)  $x = 48$ 
B)  $x = 6$ 
C)  $x = 1$ 
D)  $x = 8$ 
E)  $x = 7$

Question 18

Solve the logarithmic equation. Round your answer to two decimal places. $$\log _ { 10 } ( x - 9 ) + \log _ { 10 } x = 3$$

Accepted Answer

A)  $x = 36.44$ 
B)  $x = 495.50$ 
C)  $x = - 27.44$ 
D)  $x = 36.44 , x = - 27.44$ 
E) there is no solution 
A)  $x = 36.44$ 
B)  $x = 495.50$ 
C)  $x = - 27.44$ 
D)  $x = 36.44 , x = - 27.44$ 
E) there is no solution

Question 19

Find $( f \circ g ) ( x )$ where $f ( x ) = 4 x - 3$ and $g ( x ) = \sqrt { x + 8 }$ .

Accepted Answer

A)  $4 \sqrt { x + 8 } - 3$ 
B)  $\sqrt { 4 x + 5 }$ 
C)  $\sqrt { 4 x + 32 } - 3$ 
D)  $4 \sqrt { x + 5 }$ 
E)  $( 4 x - 3 ) \sqrt { x + 8 }$ 
A)  $4 \sqrt { x + 8 } - 3$ 
B)  $\sqrt { 4 x + 5 }$ 
C)  $\sqrt { 4 x + 32 } - 3$ 
D)  $4 \sqrt { x + 5 }$ 
E)  $( 4 x - 3 ) \sqrt { x + 8 }$

Question 20

The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function $P ( t ) = 203.0 ( 1.0107 ) ^ { t }$ , where t is the time in years with $t = 0$ corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau

Accepted Answer

A) 205.2 million 
B) 7,181.0 million 
C) 223.9million 
D) 294.6 million 
E) 1.5 million 
A) 205.2 million 
B) 7,181.0 million 
C) 223.9million 
D) 294.6 million 
E) 1.5 million

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01 t=3

Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000 dollars when invested at rate r=9% for 40 years, compounded 4 times per year. Round the answer to two decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =1

A deposit of $10,000 is placed in a savings account for 4 years. The interest for the account is compounded continuously. At the end of 4 years, the balance in the account is $12,068.34. What is the annual interest rate for this account. Round your answer to one decimal places.

Use a calculator to evaluate $\log _ { 3 } 215$ by means of the change-of-base formula. Round your answer to four decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =

Find the domain of $g \circ f$ where $f ( x ) = \sqrt { x - 2 }$ and $g ( x ) = x + 6$ .

Find $( f \circ g ) ( x )$ where $f ( x ) = 2 x + 6$ and $g ( x ) = x ^ { 2 } - 2$ .

Find the domain of $g \circ f$ where $f ( x ) = \frac { x } { x - 5 }$ and $g ( x ) = \sqrt { x }$ .

Solve the exponential equation $100,000 = 50,000 e ^ { 25 r }$ for r to determine the interest rate required for an investment of $50,000 to double in value when compounded continuously for 25 years. Round your answer to one decimal place.

An investment of $2500 is made in an account that compounds interest quarterly. After years 30 the balance in the account is $26132.78. To the nearest tenth of a percent, what is the annual interest rate for this account?

Find the domain and vertical asymptote of $g ( x ) = - \log _ { 5 } ( x + 1 )$ .

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 6 } ( x - 1 ) - \log _ { 6 } 3 = 7$

Find the domain and vertical asymptote of $f ( x ) = - \log _ { 2 } x + 3$ .

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.07 t=1

Evaluate the logarithm. $\log _ { 6 } ( - 6 )$

Solve the equation. Do not use a calculator. $\log _ { 6 } 8 x = \log _ { 6 } 48$

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 10 } ( x - 9 ) + \log _ { 10 } x = 3$

Find $( f \circ g ) ( x )$ where $f ( x ) = 4 x - 3$ and $g ( x ) = \sqrt { x + 8 }$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Exponential and Logarithmic Functions

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01 t=3

Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000 dollars when invested at rate r=9% for 40 years, compounded 4 times per year. Round the answer to two decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =1

A deposit of $10,000 is placed in a savings account for 4 years. The interest for the account is compounded continuously. At the end of 4 years, the balance in the account is $12,068.34. What is the annual interest rate for this account. Round your answer to one decimal places.

Use a calculator to evaluate log⁡3215\log _ { 3 } 215log3​215 by means of the change-of-base formula. Round your answer to four decimal places.

Evaluate the function as indicated. Round your answer to three decimal places. G(x) =1. x =

Find the domain of g∘fg \circ fg∘f where f(x)=x−2f ( x ) = \sqrt { x - 2 }f(x)=x−2​ and g(x)=x+6g ( x ) = x + 6g(x)=x+6 .

Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) where f(x)=2x+6f ( x ) = 2 x + 6f(x)=2x+6 and g(x)=x2−2g ( x ) = x ^ { 2 } - 2g(x)=x2−2 .

Find the domain of g∘fg \circ fg∘f where f(x)=xx−5f ( x ) = \frac { x } { x - 5 }f(x)=x−5x​ and g(x)=xg ( x ) = \sqrt { x }g(x)=x​ .

Solve the exponential equation 100,000=50,000e25r100,000 = 50,000 e ^ { 25 r }100,000=50,000e25r for r to determine the interest rate required for an investment of $50,000 to double in value when compounded continuously for 25 years. Round your answer to one decimal place.

An investment of $2500 is made in an account that compounds interest quarterly. After years 30 the balance in the account is $26132.78. To the nearest tenth of a percent, what is the annual interest rate for this account?

Find the domain and vertical asymptote of g(x)=−log⁡5(x+1)g ( x ) = - \log _ { 5 } ( x + 1 )g(x)=−log5​(x+1) .

Solve the logarithmic equation. Round your answer to two decimal places. log⁡6(x−1)−log⁡63=7\log _ { 6 } ( x - 1 ) - \log _ { 6 } 3 = 7log6​(x−1)−log6​3=7

Find the domain and vertical asymptote of f(x)=−log⁡2x+3f ( x ) = - \log _ { 2 } x + 3f(x)=−log2​x+3 .

Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.07 t=1

Evaluate the logarithm. log⁡6(−6)\log _ { 6 } ( - 6 )log6​(−6)

Solve the equation. Do not use a calculator. log⁡68x=log⁡648\log _ { 6 } 8 x = \log _ { 6 } 48log6​8x=log6​48

Solve the logarithmic equation. Round your answer to two decimal places. log⁡10(x−9)+log⁡10x=3\log _ { 10 } ( x - 9 ) + \log _ { 10 } x = 3log10​(x−9)+log10​x=3

Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) where f(x)=4x−3f ( x ) = 4 x - 3f(x)=4x−3 and g(x)=x+8g ( x ) = \sqrt { x + 8 }g(x)=x+8​ .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Use a calculator to evaluate $\log _ { 3 } 215$ by means of the change-of-base formula. Round your answer to four decimal places.

Find the domain of $g \circ f$ where $f ( x ) = \sqrt { x - 2 }$ and $g ( x ) = x + 6$ .

Find $( f \circ g ) ( x )$ where $f ( x ) = 2 x + 6$ and $g ( x ) = x ^ { 2 } - 2$ .

Find the domain of $g \circ f$ where $f ( x ) = \frac { x } { x - 5 }$ and $g ( x ) = \sqrt { x }$ .

Solve the exponential equation $100,000 = 50,000 e ^ { 25 r }$ for r to determine the interest rate required for an investment of $50,000 to double in value when compounded continuously for 25 years. Round your answer to one decimal place.

Find the domain and vertical asymptote of $g ( x ) = - \log _ { 5 } ( x + 1 )$ .

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 6 } ( x - 1 ) - \log _ { 6 } 3 = 7$

Find the domain and vertical asymptote of $f ( x ) = - \log _ { 2 } x + 3$ .

Evaluate the logarithm. $\log _ { 6 } ( - 6 )$

Solve the equation. Do not use a calculator. $\log _ { 6 } 8 x = \log _ { 6 } 48$

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 10 } ( x - 9 ) + \log _ { 10 } x = 3$

Find $( f \circ g ) ( x )$ where $f ( x ) = 4 x - 3$ and $g ( x ) = \sqrt { x + 8 }$ .