Exam 4: Exponential and Logarithmic Functions

The loudness of a sound of intensity x, measured in watts per square meter, is defined as L( $L ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$ -A company with loud machinery needs to cut its sound intensity to 26% of its original level. By how many decibels should the loudness be reduced?

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = 2 x + 2 ; \quad g ( x ) = \sqrt { x }$

Express as a single logarithm. - $\ln \frac { x ^ { 2 } + 4 x - 32 } { x - 3 } - \ln \frac { x ^ { 2 } + 5 x - 24 } { x + 3 } + \ln \left( x ^ { 2 } - 8 x + 16 \right) , \quad x > 0$

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8,000(3)-0.2t. Find the number of grams present in 2 years. If necessary, round to three decimal places.

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 5 x + 4 } { 3 }$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 8 } 0.537$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3.9 } 10$

Choose the one alternative that best completes the statement or answers the question. -How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.

Solve the equation. - $\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4$

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -11.8% compounded continuously

Find the amount that results from the investment. - $\$ 480$ invested at $16 \%$ compounded quarterly after a period of 9 years

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = 2 x , \quad g ( x ) = \frac { x } { 2 }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quad$ Find $( f \circ g ) ( 9 )$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 4 ^ { - 15 }$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $2 \ln \mathrm { e } ^ { 4.2 }$

Choose the one alternative that best completes the statement or answers the question. -If $5 ^ { x } = 6$ , what does $5 ^ { - 2 x }$ equal?

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }$

Write the word or phrase that best completes each statement or answers the question. -In a networking marketing plan for a company, each distributor is expected to recruit 3 new distributors. Jack was the first distributor hired by the company, so he is considered a level 1 distributor. The 3 people he recruits are considered level 2 distributors. The people recruited by the level 2 distributors are considered level 3 distributors, and so on. Write a function that models the number of distributors D at each level L. How many distributors would there be at the fifth level?

The function f is one-to-one. Find its inverse. - $f ( x ) = 3 x + 4$

Find the domain of the function. - $f ( x ) = \log _ { 1 / 2 } ( x + 4 )$