Exam 5: Exponential and Logarithmic Functions

Find the derivative of the function.

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $2,600, r = 6%, t = 10, compounded semiannually $__________

Solve the equation for x.

On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model , where t denotes the number of days since the beginning of the experiment. What was the initial fruit fly population in the experiment? __________ What was the maximum fruit fly population that could be expected under this laboratory condition? __________ What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________ How fast was the population changing on the 20th day? Please give the answer as an integer. __________

Find the second derivative of the function.

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 16% / year. Round your answer to the nearest hundredth. __________%

Find the interest rate needed for an investment of $3,000 to grow to an amount of $7,500 in 3 year(s) if interest is compounded monthly. Round your answer to two decimal places.

Online retail sales stood at $23.5 billion for 2000. For the next 2 years, they grew by 33% and 27.6% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.2%, 19.8%, 24.9%, 13.8%, 17.4%, and 10.4% per year, respectively. What are the projected online sales for 2008?

Solve the equation for x.

Simplify the expression.

Find the inflection points of the function .

Use the curve-sketching guideline, to select the graph of the function.

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 20% / year.

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth. 8% / year compounded monthly __________ % 8% / year compounded daily __________ %

A condominium complex was purchased by a group of private investors for $1.5 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment.

Find the second derivative of the function.

Find the derivative of the function.

At an annual inflation rate of 8.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to the nearest hundredth. __________ year(s)

Use the fact that log 7 = 0.8451 to find the value of the logarithm.

Use the definition of a logarithm to prove . Hint: Let and . Then, and .