Exam 5: Exponential and Logarithmic Functions

Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year.

Given that a quantity Q(t) exhibiting exponential decay is described by the function where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education. If 7 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent. ​ 13)5% compounded quarterly _________ ​ 13)5% compounded continuously _________ ​

Find the derivative of the function. ​ ​

Find an equation of the tangent line to the graph of at the point .

At an annual inflation rate of 9.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to two decimal places. ​

Find the inflection points of the function .

Simplify the expression. ​ ​

Find the second derivative of the function. ​ ​

Use logarithmic differentiation to find the derivative of the function. ​

Sketch the graphs of the functions on the same axes. ​ , , and ​

​Express the equation in logarithmic form. ​ ​

Sketch the graph of the equation. ​ ​

The radioactive element polonium decays according to the law , where Q​₀ is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present? ​ __________ mg

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 = $2,400, r = 9%, t = 10, compounded semiannually ​ $__________

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? ​

The Ehrenberg equation gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age. ​ Round your answer to the nearest tenth. ​ What is the average weight of a 10-year-old child who stands at 1.4 m tall? ​ ________ kg ​ Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.4 m to 1.45 m. ​ ________ kg

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education. If 7 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent. ​ 13.5 compounded quarterly ​ $__________ ​ 13.5 compounded continuously ​ $__________

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? __________ ​ How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________

How long will it take an investment of $8,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to the nearest tenth. ​ __________ year(s)