Exam 4: Exponential and Logarithmic Functions

Solve the problem. -The logistic growth model $P ( t ) = \frac { 290 } { 1 + 35.25 e ^ { - 0.188 t } }$ represents the population of a species introduced into a new territory after t years. What will the population be in 30 years?

Find the value of the expression. -Let $\log _ { b } A = 3$ and $\log _ { b } B = - 4$ . Find $\log _ { b } A B$ .

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function $M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$ -What is the magnitude of an earthquake whose seismographic reading is 7.6 millimeters at a distance of 100 kilometers from its epicenter?

Solve the equation. - $e ^ { x + 8 } = 4$

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to double an investment in 10 years?

Express as a single logarithm. - $5 \log _ { a } q - \frac { 5 } { 4 } \log _ { a } r + \frac { 1 } { 3 } \log _ { a } f - 3 \log _ { a } p$

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?

Solve the equation. - $125 ^ { x } = 625$

Graph the function. - $f ( x ) = \frac { 1 } { 5 } \cdot 5 ^ { x }$ A) B) C) D)

Find the amount that results from the investment. -$12,000 invested at 5% compounded quarterly after a period of 2 years

Change the exponential expression to an equivalent expression involving a logarithm. - $16 ^ { 3 / 2 } = 64$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = 2 x + 2 ; \quad g ( x ) = \sqrt { x }$

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

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { \sqrt { 3 } } 96.4$

Solve the problem. -The formula $D = 8 e ^ { - 0.6 h }$ can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. The drug is to be administered again when the amount in the bloodstream reaches 4 milligrams. What is the time between injections?

The function f is one-to-one. Find its inverse. - $f ( x ) = x ^ { 2 } + 1 , x \geq 0$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln 200$

Solve the problem. -A rumor is spread at an elementary school with 1200 students according to the model N = 1200(1 - e-0.16d) where N is the number of students who have heard the rumor and d is the number of days that have elapsed since the rumor began. How many days must elapse for 500 to have heard the rumor?

Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$