Exam 4: Inverse, Exponential, and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. -How long will it take for $\$ 1600$ to grow to $\$ 24,300$ at an interest rate of $4.4 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.

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. - $100 \log _ { 10 } 5$

Solve the problem. -How long will it take for $2100 to grow to $45,800 at an interest rate of 3.3% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Determine whether the statement is true or false. -The function $f ( x ) = m x + b$ is a one-to-one function for all values of m and b.

Graph the exponential function using transformations where appropriate. - $f(x)=2^{x+3}-2$

Find the value. Give an approximation to four decimal places. -ln 215

Solve the equation. - $\log _ { 5 } x = 3$

Write in logarithmic form. - $6 ^ { 2 } = 36$

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

Find the value. Give an approximation to four decimal places. - $\log ( 340 \times 30 )$

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ as needed. -Find the $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ if the $\mathrm { pH } = 2.3$ .

Write the word or phrase that best completes each statement or answers the question. -What is the domain of the function $y = \log _ { 8 } x$ ?

Solve the problem. -How long must $5700 be in a bank at 5% compounded annually to become $10,748.20? (Round to the nearest year.)

Solve the equation. - $\left( \frac { 256 } { 81 } \right) ^ { x + 1 } = \left( \frac { 3 } { 4 } \right) ^ { x - 1 }$

Find the future value. -$3364.54 invested for 9 years at 3% compounded monthly

Solve the equation. - $81 ^ { x } = 3$

Graph the function. Give the domain and range. -

Solve the problem. -If $f ( x ) = e ^ { x }$ , find $f \left[ \ln \left( \frac { 1 } { e ^ { 3 } } \right) \right]$

Solve the problem. -An earthquake had an intensity $104.7$ times more powerful than a reference level earthquake, or $104.7$ . $\mathrm { I } _ { 0 }$ . What was the magnitude of this earthquake on the Richter scale? $\mathrm { R } = \log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$ .