Transcript Alg 2 (6.1)rf

Exponential Growth and Decay
Objective: Determine the multiplier
for exponential growth and decay.
.08
729
.024
81 64  5184
.0001
24  8  192
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
200 400 800 1600
t  0,25 1
t  1,25  2
t  2,25  4
t  3,25  8
t  4,25 16
200 400 800 1600
t  0,25 1
t  0,25  2 0
t  1,25  2
t  1,25  21
t  2,25  4
t  2,25  2 2
t  3,25  8
t  3,25  23
t  4,25 16
t  4,25  2 4
t  n,25  2n
200 400 800 1600
t  0,25 1
t  0,25  2 0
t  1,25  2
t  1,25  21
t  2,25  4
t  2,25  2 2
t  3,25  8
t  3,25  23
t  4,25 16
t  4,25  2 4
t  n,25  2n
t  10,25  210
t  20,25  220
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. 162,661,000(1.077) 2  188,700,000
• 2016 is 2 decades, so n = 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. 162,661,000(1.077) 2  188,700,000
• 2016 is 2 decades, so n = 2.
• 2020 is 2.4 decades, so n = 2.4.
162,661,000(1.077) 2.4  194,400,000
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.
300(.80)  192mg
2
300(.80) 7  62.9mg
Homework
• Pages 358-359
• 15-41 odd, 47