Exam 5: Exponential and Logarithmic Functions

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. __________

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 6% / year compounded monthly $__________ 9% / year compounded daily $__________

Evaluate the expression.

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Please round the answer to two decimal places. __________ years

The U.S. population is approximated by the function , where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2050 (t = 4)? Round your answer to one decimal place. __________ million

The radioactive element polonium decays according to the law , where is the initial amount and the time t is measured in days. If the amount of polonium left after 420 days is 80 mg, what was the initial amount present? __________ mg

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function is continuous for all .

Simplify the expression.

Use logarithmic differentiation to find the derivative of the function.

Evaluate the expression.

Solve the equation for x.

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

Sketch the graphs of the given functions on the same axes.

The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter Round your answer to the nearest hundredth. How long would it take for the concentration of the drug in the organ to reach 0.15 __________ seconds How long would it take for the concentration of the drug in the organ to reach 0.12 __________ seconds

Evaluate the expression. = __________

Find the derivative of the function.

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 measured in decades, with corresponding to the beginning of 1960. What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place. __________ % How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places. __________ % / year Find the year when the percent of lay teachers was increasing most rapidly.

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . How long would it take for the concentration of the drug in the organ to reach 0.18 ? Please round the answer to two decimal places.

Use the laws of logarithms to simplify the expression.

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