Exam 4: Inverse, Exponential, and Logarithmic Functions

Solve the problem. -The population growth of an animal species is described by $\mathrm { F } ( \mathrm { t } ) = 400 \log ( 2 \mathrm { t } + 3 )$ where $t$ is measured in months. Find the population of this species in an area 6 months after the species is introduced.

Solve the equation and express the solution in exact form. - $\ln ( 24 x + 3 ) = \ln 9$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = \frac { 9 } { x - 7 }$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 9 }$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\log ( x - 3 ) - 2 = x ^ { 2 } - 14 x + 45$

Given $\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$ find the logarithm without using a calculator. - $\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$

Graph the function. - $f(x)=4|x|$

Determine whether or not the function is one-to-one. -

Solve the problem. -Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $u$ and $\mathrm { v }$ without using the function $\ln$ . $\ln \left( b ^ { 4 } \sqrt [ 3 ] { a } \right)$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -ex = 10

Use properties of logarithms to evaluate the expression. - $\log _ { 10 } ( 0.01 ) ^ { 8 }$

Solve the problem. -Find the required annual interest rate, to the nearest tenth of a percent, for $1100 to grow to $1400 if interest is compounded monthly for 7 years.

Write the word or phrase that best completes each statement or answers the question. - $\text { Explain how the graph of } y = \log _ { 3 } ( x + 8 ) \text { can be obtained from the graph of } y = \log _ { 3 } x \text {. }$

Find the value. Give an approximation to four decimal places. -ln 0.985

Solve for the indicated variable. - $\mathrm { I } = \mathrm { I } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 900 }$ , for $\mathrm { t }$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. - $\frac { 1 } { 2 } \log _ { 2 } x ^ { 4 } + \frac { 1 } { 4 } \log _ { 2 } x ^ { 4 } - \frac { 1 } { 6 } \log _ { 2 } x$

Find the future value. -$4498 invested for 4 years at 4.4% compounded quarterly

Solve the problem. -What is the rate on an investment that doubles $5777 in 16 years? Assume interest is compounded quarterly.

Solve the equation. Give the answer in exact form. - $2 \mathrm { e } ^ { 2 \mathrm { x } } + 3 \mathrm { e } ^ { \mathrm { x } } = 20$