Exam 5: Exponential and Logarithmic Functions

A bank credit card charges interest at the rate of 16% per year, compounded monthly.If a senior in college charges her last tuition bill of $1,700 and intends to pay it in one year, what will she have to Pay?

In a city with a population of 1,200,000, there are currently 1000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula $P = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }$ how many people will be infected in 8 years?

A cloth fragment is found in an ancient tomb.It contains 78% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially.How old is the cloth?

Use a calculator to find the value to four decimal places. $6 ^ { \sqrt { 11 } }$

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $1,000 if interest is paid at A rate of 6% per year, compounded semiannually, for 7 years.

A Wisconsin lake is stocked with 9,500 bluegill. The population is expected to grow exponentially according to the model $P = P _ { \mathrm { o } } 2 ^ { \nu / 2 }$ . How many bluegill will be in the lake in 6 years?

True or False? $\log _ { f } 4 = \log _ { 4 } f$

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 $2,600 is invested each year in an annuity earning 14% annual interest, when will the account be Worth $30,000?

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 $1,300 and intends to pay it in one year, what will she have to Pay?

A bacterial culture grows according to the formula $P = P _ { \mathrm { o } } a ^ { t }$ . If it takes 8 days for the culture to triple in size, how long will it take to double in size?

$\text { Find the db gain of an amplifier whose input voltage is } 1.3 \text { volts and whose output voltage is } 24 \text { volts. }$

A town's population grows at the rate of $4 \%$ per year. If this growth rate remains constant, how long will it take the population to double?

True or False? $\log _ { a } 7 = \log _ { 7 } a$