Exam 4: Exponential and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. -Data representing the price and quantity demanded for hand-held electronic organizers were analyzed every day for 15 days. The logarithmic function of best fit to the data was found to be $p = 398 - 73 \ln ( q )$ . Use this to predict the number of hand-held electronic organizers that would be demanded if the price were $\$ 275$ .

Find the domain of the function. - $f ( x ) = \log ( x - 6 )$

Find the value of the expression. -Let $\log _ { \mathrm { b } } \mathrm { A } = 2.087$ and $\log _ { \mathrm { b } } \mathrm { B } = 0.188$ . Find $\log _ { \mathrm { b } } \mathrm { AB }$ .

Choose the one alternative that best completes the statement or answers the question. -The logistic growth function $f ( t ) = \frac { 12,000 } { 1 + 199 e ^ { - 1.7 t } }$ models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 9 weeks?

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \frac { - 2 } { x + 7 } ; \quad g ( x ) = \frac { - 14 } { x }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. - $\ln x + \ln ( x + 4 ) = 1$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 8 } \frac { \sqrt [ 7 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$

Express as a single logarithm. - $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Solve the equation. - $2 ^ { x ^ { 2 } - 3 } = 64$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

Graph the function. - $y = \log _ { 1 / 4 } x$

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $e ^ { x } - \ln x = 4$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt { x - 1 }$

Write the word or phrase that best completes each statement or answers the question. -Julio figures that he can save $5000 per year. If, at the end of each year, he invests the money in a certificate of deposit (CD) which pays 7% interest annually, how much money will he have saved in six years?

Find the present value. Round to the nearest cent. -To get $5600 after 8 years at 5% compounded annually

Choose the one alternative that best completes the statement or answers the question. -The logistic growth model $\mathrm { P } ( \mathrm { t } ) = \frac { 410 } { 1 + 40 \mathrm { e } ^ { - 0.176 \mathrm { t } } }$ represents the population of a species introduced into a new territory after $t$ years. When will the population be 60 ?

Find a formula for the inverse of the function described below. -A size 4 dress in Country $C$ is size 40 in Country D. A function that converts dress sizes in Country C to those in Country D is $f ( x ) = 2 ( x + 16 )$ .

Use the horizontal line test to determine whether the function is one-to-one. -