1. 3.2 Exponential and Logistic Modeling

2. Exponential Population Model
If a populations P is changing at a constant percentage rate r each year, then
P(t) = P0 (1 + r)t
P0 = Initial Population
r = rate expressed as a decimal
t = time in years

3. Growth and Decay Factors
P(t) = P0 (1 + r)t
If r > 0, then P(t) is an exponential growth function
Growth Factor = 1 + r
If r < 0, then P(t) is an exponential decay function
Decay Factor = 1 + r

4. Finding growth and decay rates: Exponential growth or decay function
Finding growth and decay rates: Exponential growth or decay function? Find constant percentage rate of growth/decay.
f(x) = 78,963  0.968x
g(t) = 247  2t
You Try!
P(t) = 3.5  1.09t

5. Finding an Exponential Function:
Initial population = 28,900, decreasing at a rate of 2.6% per year
You Try!
Initial Height = 18 cm, growing at a rate of 5.2% per week

6. Find the logistic function that satisfies the given conditions:
Initial Value = 10; Limit to Growth = 40; Passing through (1,20)

7. You Try! Find the logistic function that satisfies the given conditions:
Initial Population = 16; Maximum Sustainable Population = 128; Passing through (5,32)

8. Estimate the population in 1915 and 1940
You Try! Exponential Growth: The population of Smallville in the year 1890 was Assume the population increased at a rate of 2.75% per year.
Estimate the population in 1915 and 1940
Predict when the population reached 50,000

9. Radioactive Decay: The half-life of a certain radioactive substance is 14 days. There are 6.6 grams initially present.
Express that amount of substance remaining as a function of time t
When will there be less than 1 gram remaining?

10. Homework
Pg (4,8,16,24,32,42)
Chapter 3 Vocabulary Sheet Due Tomorrow