Exam 5: Exponential and Logarithmic Functions

The percent $P$ of the drug triazolam (a drug for treating insomnia) remaining in a person's bloodstream after t hours is given by $P = e ^ { - 0.3 t }$ . What percent will remain in the bloodstream after 9 hours?

Use a calculator to find the value for $\log 0.41326$ to four decimal places.

In one individual, the percent alcohol level $t$ minutes after two shots of whiskey is given by $P = 0.3 ( 1 -$ $\left. e ^ { - 0.05 t } \right)$ . Find the blood alcohol level after 26 minutes.

Solve the equation. $\log _ { 5 } x = \log _ { 5 } \frac { 1 } { x } + 8$

Solve the equation. $\log _ { 3 } x = \log _ { 3 } \frac { 1 } { x } + 6$

If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where $n = \frac { \log \left[ \frac { A r } { p } + 1 \right] } { \log ( 1 + r ) }$ If $S 5,000$ is invested each year in an annuity earning $9 \%$ annual interest, when will the account be worth $\$ 40,000$ ?

Solve the equation. $\log ( x - 50 ) - \log 9 = \log ( x - 30 ) - \log x$

Use a calculator to find the value for to four decimal places.

A Wisconsin lake is stocked with 10,000 bluegill. The population is expected to grow exponentially according to the model $P = P _ { 0 } 2 ^ { t / 2 }$ . How many bluegill will be in the lake in 6 years?

Solve the equation. $\log ( x - 46 ) - \log 6 = \log ( x - 32 ) - \log x$

Simplify the expression. $7 ^ { \log 76 }$

Simplify the expression. $8 ^ { \sqrt { 5 } } \cdot 8 ^ { \sqrt { 5 } }$

In one individual, the percent alcohol level $t$ minutes after two shots of whiskey is given by $P = 0.3 ( 1 -$ $e ^ { - 0.05 t }$ ). Find the blood alcohol level after 29 minutes.

Find the db gain of an amplifier whose input voltage is 0.7 volts and whose output voltage is 17 volts.

If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where $n = \frac { \log \left[ \frac { A r } { P } + 1 \right] } { \log ( 1 + r ) } .$ If $\$ 7,000$ is invested each year in an annuity earning $6 \%$ annual interest, when will the account be worth $\$ 55,000 ?$

A bank credit card charges interest at the rate of 15% per year, compounded monthly.If a senior in college charges her last tuition bill of $1,100 and intends to pay it in one year, what will she have to Pay?

Solve the equation. $2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 112 )$

Solve the equation. $2 \log _ { 2 } x = 1 + \log _ { 2 } ( x + 40 )$

An account now contains $11,300 and has been accumulating interest at a 9% annual rate, compounded continuously, for 9 years.Find the initial deposit.