Exam 6: Exponential and Logarithmic Functions

If $6,000 is invested at an annual rate of 9% per year compounded monthly, the future value S at any time t (in months) is given by . What is the amount after 1 year? Round your answer to the nearest cent. ​

Use the formula . In October 2004, an earthquake measuring 6.8 on the Richter scale occurred in Japan. The largest quake in Japan since 1990was one in 1993that registered 7.7. How many times more severe was the 1993shock than the one in 2004on the Richter scale? Round your answer to one decimal place. ​

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place. ​

Solve the exponential equation. Give answers correct to 3 decimal places. ​ ​

The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers, with x representing years past 1900. Find an equation that models these data. If it's necessary, round your calculations to four decimal places. ​ ​ Source: U.S. Bureau of the Census ​

Graph the function. ​ ​

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. ​ ​

Graph the function. ​ ​

Graph the function. ​ ​

If the supply function for a product is given by , where q represents the number of hundreds of units, what will be the price when the producers are willing to supply 500 units? Round your answer to the nearest cent. ​

The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. Determine the monthly sales 4 months after the promotional campaign. Round your answer to the nearest cent. ​

For selected years from 1978 to 2002, the number of mutual funds N, excluding money market funds, can be modeled by , where t is the number of years past 1975 (Source: Investment Company Institute, Mutual Fund Fact Book (2003)). Use the model to estimate the year when the number of mutual funds will reach 8,000. ​

By using data from the U.S. Bureau of Labor Statistics for the years 1968-2002, the purchasing power P of a 1983 dollar can be modeled with the function , where t is the number of years past 1960. In what year will the purchasing power of a 1983 dollar be $0.10? Round-up your answer to the nearest year. ​

Write the equation in exponential form. ​ ​

By using data from the U.S. Bureau of Labor Statistics for the years 1968-2002, the purchasing power P of a 1983 dollar can be modeled with the function , where t is the number of years past 1960. Based on this model, what is the purchasing power of a 1983 dollar in the year 1970? Round your answer to the nearest cent. ​

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. ​ ​

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . How long will it be before a pension of $60,000 per year has a purchasing power of $30,000? Round your answer to one decimal place. ​

Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer two decimal places. ​ ​ ​

For selected years from 1960 to 2001, the national health care expenditures H, in billions of dollars, can be modeled by , where t is the number of years past 1960 (Source: U.S. Department of Health and Human Services). If this model remains accurate, in what year will national health care expenditures reach $3 trillion (that is, $3000 billion)? Round your answer to the nearest year. ​

Solve the exponential equation. Give the answer correct to 3 decimal places. ​ ​