Exponential Growth and Decay Objective: Determine the multiplier for exponential growth and decay

Exponential Growth and Decay

Objective: Determine the multiplier for exponential growth and decay.

08. 024. 0001.

729 51846481 192824

Application: Biology

• Bacteria are very small single-celled organisms that live almost everywhere on Earth. Most bacteria are not harmful to humans, and some are helpful, such as the bacteria in yogurt.

Application: Biology

• Bacteria are very small single-celled organisms that live almost everywhere on Earth. Most bacteria are not harmful to humans, and some are helpful, such as the bacteria in yogurt.

• Bacteria reproduce, or grow in number, by dividing. The total number of bacteria at a given time is referred to as the population of bacteria. When each bacterium in a population of bacteria divides, the population doubles.

200 400 800 1600

200 400 800 1600

1625,4

825,3

425,2

225,1

125,0

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200 400 800 1600

1625,4

825,3

425,2

225,1

125,0

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t

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4

3

2

1

0

225,4

225,3

225,2

225,1

225,0

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tnnt 225,

200 400 800 1600

1625,4

825,3

425,2

225,1

125,0

t

t

t

t

t

4

3

2

1

0

225,4

225,3

225,2

225,1

225,0

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20

10

225,20

225,10

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nnt 225,

200 400 800 1600

Exponential Expressions

Modeling Human Population Growth

• Human populations grow much more slowly than bacterial populations. Bacterial populations that double each hour have a growth rate of 100% per hour. The population of the United States in 1990 was growing at a rate of about 8 % per decade.

Example 1

Example 1

Example 1

Example 1

Try This

• The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020.

Try This

• The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020.

• The starting population is 162,661,000.• The multiplier is 1.077.• 2016 is 2 decades, so n = 2.

000,700,188)077.1(000,661,162 2

Try This

• The population of Brazil was about 162,661,000 in 1996 and was projected to grow at a rate of about 7.7% per decade. Predict the population, to the nearest hundred thousand, of Brazil for 2016 and 2020.

• The starting population is 162,661,000.• The multiplier is 1.077.• 2016 is 2 decades, so n = 2.• 2020 is 2.4 decades, so n = 2.4.

000,400,194)077.1(000,661,162 4.2

000,700,188)077.1(000,661,162 2

Modeling Biological Decay

Modeling Biological Decay

Example 2

Example 2

Try This

• 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 milligrams. 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.

Try This

• 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 milligrams. 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.

• We start with 300, and the multiplier is .80.

mg192)80(.300 2 mg9.62)80(.300 7

Homework

• Pages 358-359• 15-41 odd, 47