Exam 5: Exponential and Logarithmic Functions

Use logarithms to solve the equation for t. Round your answer to four decimal places. ​ ​

Simplify the expression. ​ ​

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be . ​ What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place. ​ __________%

Find the second derivative of the function. ​ ​

Find the derivative of the function. ​ ​

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places. ​

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth. ​ __________%

Evaluate the expression. ​ __________

How long will it take an investment of $4,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to the nearest hundredth. ​ __________ year(s)

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 16% / year. Round your answer to two decimal places. ​

Find the derivative of the function. ​ ​

At an annual inflation rate of 5.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to the nearest hundredth. ​ __________ year(s)

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. __________

The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t is measured in decades, with corresponding to the beginning of 1960. ​ Find the year when the percent of lay teachers was increasing most rapidly. ​

Find the derivative of the function. ​ ​

Use the definition of a logarithm to prove . ​

Write the expression as the logarithm of a single quantity. ​

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by ​ . ​ How fast is the price of the commodity changing at ? ​

Solve the equation for ​ . ​​ __________

Find the derivative of the function. ​