Exam 5: Exponential and Logarithmic Functions

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

Rewrite as a single logarithm. - $6 \log _ { q } q - \log _ { q } r$

Graph the function. - $f ( x ) = \log _ { 5 } ( x - 3 )$

How long would it take $5000 to grow to $25,000 at 9% compounded continuously? Round your answer to the nearest tenth of a year.

In the formula A(t) $\mathrm { A } ( \mathrm { t } ) = \mathrm { A } _ { 0 } \mathrm { e } ^ { k t }$ , A is the amount of radioactive material remaining from an initial amount $\mathrm{A}_{0}$ at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope Decays at a rate of 0.125% annually. Determine the half-life of this isotope, to the nearest year.

$4 ( 5 x - 1 ) = 18$ Round to three decimal places.

Provide an appropriate response. -With the exponential function f(x) $f ( x ) = a ^ { x } , \text { why must } a \neq 1$

Evaluate the function. Round to two decimal places. -Evaluate $\frac { 30 } { 1 + 2 \mathrm { e } ^ { - \mathrm { x } } } \text { when } \mathrm { x } = 4$

The natural resources of an island limit the growth of the population to a limiting value of 3423. The population of the island is given by the logistic equation $\mathrm { P } ( \mathrm { t } ) = \frac { 3423 } { 1 + 4.25 \mathrm { e } ^ { - 0.31 t } }$ where t is the number of years after 2010. What would be the predicted population of the island in 2019?

The number of students infected with the flu on a college campus after t days is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 600 } { 1 + 39 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$ When will the number of infected students be 300?

Evaluate the logarithm, if possible. Round the answer to four decimal places. -log 169

Graph the function. - $f(x)=\ln x$

Graph the function. - $f ( x ) = 120 ( 0.02 ) ^ { 0.5 ^ { x } }$

A certain noise measures 79 decibels. If the intensity is multiplied by 10, how many decibels will the new noise measure? $\mathrm { L } = 10 \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$

Evaluate the logarithm, if possible. Round the answer to four decimal places. - $\log ( - 17 )$

Find the exponential function that models the data in the table below. x f(x) -2 9 -1 13.5 0 20.25 1 30.375 2 45.5625

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$

The number of employees of a company, N(t), who have heard a rumor t days after the rumor is started is given by the logistic equation $\mathrm { N } ( \mathrm { t } ) = \frac { 268 } { 1 + 51.6 \mathrm { e } ^ { - 0.25 \mathrm { t } } }$ How many employees have heard the rumor 12 days after it is Started?