Exam 4: Inverse, Exponential, and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. -The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } 0.03 \mathrm { t }$ where $\mathrm { k }$ is a constant and $\mathrm { t }$ is the time in years. If the current population is 39,000 , in how many years is the population expected to be 97,500 ?

Find the value. Give an approximation to four decimal places. - $\log \left( 6.52 \times 10 ^ { 3 } \right)$

Solve the equation. - $x = \log _ { 5 } \sqrt [ 4 ] { 125 }$

Write the word or phrase that best completes each statement or answers the question. -A population is increasing according to the exponential function defined by $\mathrm { y } = 3 \mathrm { e }^{ \cdot 04 x }$ , where $\mathrm { y }$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Determine whether or not the function is one-to-one. - $f ( x ) = x ^ { 2 } - 2$

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 2 } - 9 ; x \geq 0$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = \sqrt [ 3 ] { x + 2 }$

Solve the equation. Round to the nearest thousandth. - $2 ( x - 2 ) = 9$

Find the value. Give an approximation to four decimal places. -ln(729 × 25)

Find the value. Give an approximation to four decimal places. -ln 45,600,000

Find the value. Give an approximation to four decimal places. - $\log 2.66$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 5.4 } 2.6$

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

Solve the equation and express the solution in exact form. - $\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$

Graph the function. - $f(x)=3^{x}$

Find the present value of the future value. -$10,000, invested for 5 years at 3% compounded quarterly

Solve the equation. - $x = 9 ^ { \log _ { 9 } 12 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt [ 3 ] { 7 x - 1 }$

Solve the problem. -Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the function $\ln$ . $\ln \left( \sqrt [ 5 ] { a b ^ { 6 } } \right)$

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