Exam 5: Exponential and Logarithmic Functions

The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What is the expected upper limit on sales? ​

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation . Graph this function with a graphing utility. Which of the following statements best describes the situation after 10 hours? ​

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data and then use the model to predict when 59.4% of the U.S. population will have internet connections. Use x as the number of years past 1995. Round your answer to the nearest year. ​

Suppose the supply of x units of a product at price p dollars per unit is given by . How many units would be supplied when the price is $50 each? Round your answer to one decimal place. ​

Given , use a graphing calculator to graph for and . ​

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. ​

Solve the exponential equation. Round your answer to three decimal places, if necessary. ​ ​

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. ​

Given . Graph and for . ​

Use the properties of logarithms to write the expression as a single logarithm. ​ ​

Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary. ​ ​

Graph the function. ​ ​

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

Use a calculator to evaluate the expression. Round your answer to two decimal places. ​ ​

Total personal income in the United States (in billions of dollars) for selected years from 1960 to 2002 is given in the following table. ​​ Source: Bureau of Economic Analysis, U.S. Department of Commerce These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years past 1960. If this model is accurate, what will be the total U.S. personal income in 2010? Round your answer to two decimal places. ​

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

Solve the logarithmic equation . ​

Suppose that the equation represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at t = 0)? ​

If the total cost (in dollars) for x units of a product is given by , what is the total cost of producing 150 units? 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 1990 was one in 1993 that registered 7.7. How many times more severe was the 1993 shock than the one in 2004 on the Richter scale? Round your answer to one decimal place. ​