Exam 5: Exponential and Logarithmic Functions

The number of acres in a landfill is given by the function $B = 2900 \mathrm { e } ^ { - 0.05 t }$ where t is measured in years. How many acres will the landfill have after 8 years? (Round to the nearest acre.)

Find the function value. -Let $f ( x ) = 5 ^ { x }$ . Find $f ( - 2 )$ .

Provide an appropriate response. -What is the domain of the function $y = \log _ { 6 } x$ ?

$20 ^ { x } = 54$ Round to two decimal places.

Evaluate the logarithm, if possible. Round the answer to four decimal places. -log 0.0743

Provide an appropriate response. - $\text { Solve } S = R \left( \frac { ( 1 + i ) ^ { n } - 1 } { i } \right) \text { for } R$

The half-life of Titanium 45 is $3.1$ hours. If the formula $\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { \mathrm { t } / 3.1 }$ gives the percent (as a decimal) remaining after time $t$ (in hours), sketch $P$ versus t.

Find the least amount that could be deposited in a bank account today at 8% compounded semiannually to allow $1,875 withdrawals at the end of each 6 months for 12 years.

Prices in an economy with a 12% annual inflation rate can be modeled by P $\mathrm { P } = p \mathrm { e } ^ { \mathrm { rt } }$ , where r is the inflation rate, t is the time in years, and p is the current price. How long will it take for prices in the economy to double at a 12% annual inflation rate?

Find the function value. -Let $f ( x ) = 3 ( 1 - x )$ . Find $f ( 3 )$ .

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

Find the least amount that could be deposited in a bank account today at 12% compounded quarterly to allow $650 withdrawals at the end of each quarter for 10 years.

Find the function value. - $\text { Let } f ( x ) = e ^ { - x } \text {. Find } f ( 3.9 ) \text {, rounded to four decimal places. }$

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { a } 8 x ^ { 3 } y z ^ { 5 }$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -log (x+10)-log (x+4)=log x

A pair of rabbits are introduced on a small island, and the population grows until the food supply and natural enemies of the rabbits on the island limit the population. If the number of rabbits is $\mathrm { N } = \frac { 200 } { 1 + 75 \left( 2 ^ { - 0.7 t } \right) }$ where t Is the number of years after the rabbits are introduced, how long does it take for the rabbit population to reach 100?

Graph the function. - $f ( x ) = \log _ { 2 } x + 4$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $4 ^ { x } > 16$

Graph the function. - $y=\log _{2} x$

Sumi Kato's savings account has a balance of $3950. After 13 years, what will the amount of interest be at 5.5% compounded annually?