Exponential Growth and Decay

1. Exponential Growth and Decay Objectives: Determine the multiplier for exponential growth and decay Write and evaluate exponential expressions to model growth and decay situations

2. Modeling Bacteria Growth Time (hr) 0 1 2 3 4 6 5 Population 25 50 100 200 400 1600 800 Write an algebraic expression that represents the population of bacteria after n hours. The expression is called an exponential expression because the exponent, n is a variable and the base, 2, is a fixed number. The base of an exponential expression is commonly referred to as the multiplier.

3. Example 1 Find the multiplier for each rate of exponential growth or decay. a) 9% growth = 1.09 100% + 9% = 109% b) 0.08% growth = 1.0008 100% + 0.08% = 100.08% c) 2% decay = 0.98 100% - 2% = 98% d) 8.2% decay = 0.918 100% - 8.2% = 91.8%

4. Example 2 Suppose that you invested $1000 in a company’s stock at the end of 1999 and that the value of the stock increased at a rate of about 15% per year. Predict the value of the stock, to the nearest cent, at the end of the years 2004 and 2009. Since the value of the stock is increasing at a rate of 15%, the multiplier will be 115%, or 1.15 = $2011.36 = $4045.56

5. Example 3 Suppose that you buy a car for $15,000 and that its value decreases at a rate of about 8% per year. Predict the value of the car after 4 years and after 7 years. Since the value of the car is decreasing at a rate of 8%, the multiplier will be 92%, or 0.92 = $10,745.89 = $8,367.70

6. Practice A vitamin is eliminated from the bloodstream at a rate of about 20% per hour. The vitamin reaches a peak level in the bloodstream of 300 mg. Predict the amount, to the nearest tenth of a milligram, of the vitamin remaining 2 hours after the peak level and 7 hours after the peak level.