Exam 5: Exponential and Logarithmic Functions

An earthquake was recorded as $10 ^ { 6.5 }$ times more powerful than a reference level zero earthquake. What was the magnitude of this earthquake on the Richter scale? $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ .

Graph the function. - $f ( x ) = \frac { 43 } { 1 + 5 e ^ { - x } }$

Evaluate the logarithm, if possible. Round the answer to four decimal places. -ln 5,500,000

Provide an appropriate response. -Explain how this statement needs to be changed so that it is true: $\log _ { 3 } ( 8 + 8 ) = \log _ { 3 } 8 + \log _ { 3 } 8$

The number of periods needed to double an investment when a lump sum is invested at 2%, compounded semiannually, is given by n $\mathrm { n } = \frac { \ln 2 } { \ln 1.01 }$ . Find the number of years before the investment doubles in value, to the Nearest tenth of a year.

Provide an appropriate response. -What is the range of the function $y = \log _ { 4 } x ?$

Match the equation with its graph. - $y = \frac { 1 } { 3 } \cdot 3 ^ { x }$

Write the logarithmic equation in exponential form. - $\log _ { 2 } ( 8 ) = 3$

Find an exponential function that models the data below and use it to predict about how many books will have been read in the eighth grade. Grade Number of Books Read 2 9 3 27 4 67 5 121

You have money in an account at 5% interest, compounded weekly. To the nearest year, how long will it take for your money to triple?

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - $\mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { k } } \right) ^ { \mathrm { kn } } \text { for } \mathrm { P } = \$ 14,000 , \mathrm { n } = 12 , \mathrm { r } = 5 \% , \mathrm { k } = 2$

Use the formula R $R = \log \left( \frac { \mathrm { I } } { \mathrm { I } 0 } \right)$ , where the magnitude of an earthquake on the Richter scale is based on I, the measurement of a seismic wave, and I0, the measurement of a seismic wave of a level zero earthquake with the Same epicenter. If an earthquake measured 5.3 on the Richter scale, what was the intensity of the earthquake? (Round to whole number.)

Provide an appropriate response. -Select an appropriate type of modeling function for the data shown in the graph. Choose from exponential, logarithmic, and linear.

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $512 ^ { x } < 8$

An animal species is introduced into a certain area. Its population is approximated by $F ( t ) = 400 \log ( 2 t + 3 )$ , where t represents the number of months since its introduction. Find the population of this species 6 months After its introduction into the area. Round your answer to the nearest whole number.

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log _ { 6 } ( 16.58 )$

Use the formula R $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ , where the magnitude of an earthquake on the Richter scale is based on I, the measurement of a seismic wave, and I0, the measurement of a seismic wave of a level zero earthquake with the Same epicenter. An earthquake was recorded which was 2,511,886 times more powerful than a reference level Zero earthquake. What is the magnitude of this earthquake? (Round to the nearest tenth.)

Find the present value of a loan with an annual interest rate of 6.3% and periodic payments of $749.94 for a term of 8 years, with payments made and interest charged 12 times per year.

Rewrite as a single logarithm. - $\left( \log _ { t } t - \log _ { t } s \right) + 5 \log _ { t } u$

Write in logarithmic form. - $6 ^ { 3 } = 216$