6.1 Exponential Growth and 6.1 Exponential Growth and DecayDecay

6.1 Exponential Growth and 6.1 Exponential Growth and DecayDecay

Objectives: •Determine the multiplier for exponential growth and decay•Write and evaluate exponential expressions to model growth and decay situations

Write an algebraic expression that represents the population of bacteria after n hours.

Modeling Bacteria Growth

n25 2

Time (hr)

Population

0 1 2 3 4 5 6

25 50 100

200 400 800 1600

The expression is called an exponential expression because the exponent, n is a variable and the base, 2, is a fixed number.

n25 2

The base of an exponential expression is commonly referred to as the multiplier.

Example 1Find the multiplier for each rate of exponential growth or decay.

a) 9% growth 100%

+ 9%

= 109%

= 1.09

b) 0.08% growth

100%

+ 0.08%= 100.08%

= 1.0008

c) 2% decay 100%

- 2%

= 98%

= 0.98

d) 8.2% decay 100%

- 8.2%= 91.8%

= 0.918

Example 2Suppose 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.

n1000 (1.15)

Since the value of the stock is increasing at a rate of 15%, the multiplier will be 115%, or 1.15

51000 (1.15)

101000 (1.15)

= $2011.36

= $4045.56

Example 3Suppose 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.

n15000 (0.92)

Since the value of the car is decreasing at a rate of 8%, the multiplier will be 92%, or 0.92

415000 (0.92)

715000 (0.92)

= $10,745.89

= $8,367.70

PracticeA 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.

Homework

Lesson 6.1 # 15, 17, 23, 37, 39, 41-51 (all), and 71.