Exam 5: Exponential and Logarithmic Functions

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly.His investment is now worth $24,204.54.How much did he originally invest? Round your answer to the nearest cent. $__________

Solve the equation for x.

Evaluate the expression.

The height (in feet) of a certain kind of tree is approximated by where is the age of the tree in years.Estimate the age of a 90-ft tree.Round your answer to the nearest hundredth. __________ years

Find the derivative of the function.

Evaluate the expression.

Find the present value of $57,939 due in 6 year(s) at an interest rate of 9% / year compounded continuously.Round your answer to the nearest integer.

Determine the intervals of concavity for the function.

Use logarithmic differentiation to 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 = $2,500, r = 6%, t = 15, compounded semiannually

Find the derivative of the function.

Use logarithms to solve the equation for t.Please round the answer to four decimal places.

The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?

Find the effective rate corresponding to the given nominal rate.Round your answers to two decimal places. 15% / year compounded semiannually _____% 9% / year compounded quarterly _____%

Find the derivative of the function.

Solve the equation for x.

Find the derivative of the function.

The length (in centimeters) of a typical Pacific halibut t years old is approximately .What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.

Three hundred students attended the dedication ceremony of a new building on a college campus.The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational.The number of students who learned of the new program t hours later is given by the function . If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?

Use the definition of a logarithm to prove