Exam 5: Exponential and Logarithmic Functions

Simplify the expression.

Use the facts that log 3 = 0.4771 and log 4 = 0.6021 to find the value of the logarithm.Round your answer to four decimal places. log 12

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 3 years?

Find the derivative of the function.

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . Select the graph of this function.At what level is the demand expected to stabilize?

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . Find the equilibrium price of the commodity. (Hint: It's given by .Also, use the fact that .)

Express the equation in logarithmic form.

Express the equation in logarithmic form.

Evaluate the expression.

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.__________

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

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

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at t = 0? $__________ / unit How fast is the price of the commodity decreasing at t = 0? $__________ / wk Find the equilibrium price of the commodity.(Hint: It's given by .Also, use the fact that .) $__________ / unit

Use logarithmic differentiation to find the derivative of the function.

Simplify the expression.

How long will it take $5,000 to grow to $6,500 if the investment earns interest at the rate of 13% / year compounded monthly?

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

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 560 days is 40 mg, what was the initial amount present?

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to the nearest tenth. __________ year(s)