Exponential Growth

1
Exponential Growth Decay

• Constant Percentage Rate of Change
• An Epidemic ? The Logistic Function

2
Constant Percentage Rate

• Suppose a population is changing at a constant
  percentage rate.
• r constant percentage rate
• b 1 r
• Definition of Exponential Function
• Growth

3
Growth or Decay? Constant Percentage Rate?
4
Write an Exponential Function

• Initial Value 10 and
  increasing at a rate of 8 per year.
• Initial population 34,000 and
  decreasing at a rate of 7 per year.
• Initial height 14 cm and
  growing at a rate of 2.3 per week
• Initial mass 22 grams and doubling
  every 6 weeks
• Initial mass 38 grams and
  halving every other day

5
Radioactive Decay

• The half-life of a radioactive element means the
  time it takes a given amount of the element to
  decay to half that amount.
• Ex. Carbon 14 is contained
  in all living things.
• C14 has a half-life of 5730 years.

6
Logistics Model

• Some populations have unrestricted growth.
• Many populations have a limit to their growth.
• Ex the of fish in an aquarium
• the of trout in a lake
• the sick people in a
  school
• the height of a growing
  plant

7
The Logistic Function

• c limit to growth
• c / (1a) initial value
• Solve for b using another data point.

8
Find the Logistic Function

• Limit to Growth 40, Initial Value 8, and
  passing through ( 1 , 10 )
• Initial Population 15, Maximium
  Sustainable Population 224 and passing
  through ( 1 , 8 )