Exam 4: Exponential and Logarithmic Functions

The approximate lengths and diameters (in inches) of common nails are shown in the table.Find a logarithmic equation that relates the diameter of a common nail to its length

Match the function below with its graph. Graph I : Graph IV: Graph II: Graph V: Graph III:

Estimate the percentage of radioactive material that remains in a sample after 5 years if the half-life of the material is 299 days.Round to the nearest hundredth of a percent.

Write the exponential equation in its logarithmic form.

The U.S.annual gross domestic product G (in billions of dollars) from 1985 through 2009 can be modeled by where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009. (b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.

Find the inverse function informally Verify that and

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Condense the expression to the logarithm of a single term.

Find the inverse function of the function f given by the set of ordered pairs.

Solve for x.

Find the exact value of without using a calculator.

Sketch the graph of the function

Evaluate the logarithm without using a calculator.

Find the balance if $27,000 is invested at an annual rate of 6.5% for 4 years, compounded continuously.

Use the properties of logarithms to simplify the logarithmic expression below.

A stock analyst attempts to express the price p of a share of XYZ stock as an exponentially increasing function of the time since XYZ's initial public offering (IPO): , where m is the number of months since the IPO.The price of a share was $10.00 at the time of the IPO and $13.60 four months after the IPO.What is the approximate value of k? Round to the nearest thousandth.

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution.What is [H⁺] if the

Write the logarithmic equation in exponential form.

Determine whether Justify your answer.

The present value of money is the principal you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year.