Exam 6: Exponential and Logarithmic Functions

Suppose that the market share y (as a percent) that a company expects t months after a new product is introduced is given by . How long (to the nearest month) will it take for the market share to be 25%? Round your answer to one decimal place. ​

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? ​

Suppose that the market share y (as a percent) that a company expects t months after a new product is introduced is given by . What is the market share after the first month (to the nearest percent)? Round your answer to two decimal place. ​

Solve the logarithmic equation . Round your answer to three decimal places. ​

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 will the sales be when she assumes office? ​

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

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

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 57.0% 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. ​ ​ Source: U.S. Department of Commerce ​