A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050, approximately 82.6 million Americans will be at least 65. The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond. A graphing calculator screen displays an exponential function that models the U.S. population age 65 and over, y, in millions, x years after 1899. Use this information to solve (a) (d) below. Click the icon to view the bar graph. B ExpReg y = a-b^x a = 3.363809536 b = 1.023357735 a. Explain why an exponential function was used to model the population data. An exponential function was used because the data in the bar graph is increasing more and more rapidly. OB. An exponential function was used because population is always modeled using exponential functions. OC. An exponential function was used because there are too many data points to use a linear function. OD. An exponential function was used because exponential functions are always more accurate than linear functions. b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places. f(x) =

The amount of a drug in one’s bloodstream decreases by 18% every hour. Initially, 150 milligrams of the drug is administered.What is the exponential function that models the amount of the drug that remains in the bloodstream after t hours?

The world's population in 1980 was about 4.5 billion. Suppose the population increased at a rate of 2% per year since then. a) Write an exponential relation that models the problem. Explain what each variable represents. b) Use your answer to part a. to estimate the world's population in 2025. c) Use your answer to part a) to estimate the world's population in 1970. d) What assumptions are you making as you answer these questions?

Engineers are draining a water reservoir until its depth is only 10 feet. The depth decreases exponentially as shown in the graph below. The engineers measure the depth adter 1  hour to be 64 feet and after 4 hours to be 28 feet. Develop an exponential equation in y=a(b)^2 to predict the depth as a function of hours draining. Round a to the nearest integer and b to the nearest hundredth. The, graph the horizontal line y = 10 and find its intersection to determine the time, to the nearest tenth of an hour, when will the reservoir reach a depth of 10 feet?