Exponential Growth and Decay Objective: Determine the multiplier for exponential growth and decay.
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Transcript of 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
t
t
t
t
t
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
t
t
t
t
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
t
t
t
t
t
20
10
225,20
225,10
t
t
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