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MCV4U1-UNIT FIVE-LESSON THREE Lesson 3: Optimization Problems Involving Exponential Functions 1. An ant population, P t of a rare Brazilian ant is given by P t 1000e 0.3t , where t is the time in days. Find the rate of change of population when t=2 and when t=5. 2. activity is needed and is socially desirable, When a new such as waste recycling, its growth is rapid at first and then levels off. Suppose the sale of waste-recycling plants is given by St 100 90e 0.3t , where t is the time in years and St represents sales in year t. Find the rate of change of sales when t=1 and when t=10. 3. t 20 N t 2000[30 te ]. Find The number N of bacteria in a culture at time t is the largest number of bacteria in the culture during the interval 0 t 50, where t is measured in hours. 4. The net monthly profit from the sale of acertain product is given (in dollars) number of items by the formula P x 10 6 1 x 1e 0.001x , where x is the sold. a) Find the number of items that yield the maximum profit. Assume that at items can be produced per month. most 2000 b) Repeat part a) assuming that at most 500 items can be produced per month. hw: P.245-247 #4, 5, 6, 8, 12(use graphmatica), 13