The following are exercises for module 5 (Ch 5) of the learning objectives in Math 1324. 1.) A drug's effectiveness decreases over time. If each hour, a drug is only 90% as effective as during the previous hour, at some point the patient will not be receiving enough medication and will need another dose. This can be modeled by the exponential function y = y 0 (0.90)t-1 . In this equation y 0 is the amount of the initial dose, and y is the amount of the medication still available "t" hours after the drug was administered. Suppose the initial dose was 200 mg. How long will it take for this initial dose to reach the dangerously low level of 50 mg? Solve this problem algebraically, not with a graph or by plugging and checking. 2.) The sales of a product decline after the end of an advertising campaign, with the model given by S 100,000e0.5t , where t = number of weeks since the end of the campaign. During what week after the end of the campaign will sales drop below 400? Show work. 3.) In 2009, the world population was 6.8 billion. The exponential growth rate was 1.13% per year. So the following could be used as a model for the growth of the world's population: P = 6.8e0.0113t P is world population in billions. "t" represents the number of years past 2009. 2009 would be represented by t = 0. a.) Estimate the population of the world in 2014 using this model. b.) Using Google and the internet, find an approximation for the current world population. What is the difference between the estimate from the internet and the answer in part (a)? c.) Using algebraic methods and the model given, estimate the year when the world population will be 9 billion. 4.) The number of students infected with flu at Springfield High School after t days is modeled by the function P(t) = 800 1+ 49e-0.2t (a) What was the initial number of infected students? (b) When will the number of infected students be 200? (c) The school will close when 300 of the 800-student body are infected. When will the school close? 5.) The population of deer after t years in Cedar State Park is modeled by the function P(t) = 1001 1+ 90e-0.2t (a) What was the initial population of deer? (b) When will the number of deer be 600? 6.) The demand function for a piece of computer software is given by where p = the price per unit when x units are demanded.. p 850e.003 x a.) Find the price when 900 units are demanded. _________________ b.) Find the quantity demanded when the price is $40. Show your work. Math 1324 Module 5 Page 1 7.) The ACME Corporation is planning on introducing their new product, the Super Deluxe Widget 2000. They would like to reach as many people as possible by using a television advertising campaign in the city Metropolis, whose populations 3 million people. Based on prior experience, the model for the number of people N (in millions) who are aware of the product after t days of advertising was found to be N = 3(1- e-0.04t ) . a. Create a table and determine the number of people who are aware of the Super Deluxe Widget 2000 at the start of the advertising campaign, after 1 week of advertising, after 5 weeks, after 10 weeks, and after 20 weeks. b. How long will it take before 1 million people are aware of the Super Deluxe Widget 2000? c. How long will it take before 2 million people are aware of the Super Deluxe Widget 2000? Math 1324 Module 5 Page 2