November 17, 2009
3.2 Exponential and Logistic Modeling
Exponential Population Model
P(t) = P (1+r)t
time in years
0
growth/decay
factor (1+r)
percentage rate each year
initial population
Time in Years
Population
0
Po
1
initial populaton
time in years
rate each year (decimal)
2
3
r > 0, then exponential growth
r < 0, then exponential decay
November 17, 2009
Question:
If a culture of 100 bacteria is put into a petri dish and
the culture doubles every hour how long will it take to
reach 400,000?
November 17, 2009
November 17, 2009
November 17, 2009
Given: f(x) = 5500 0.9968x
Exponential growth or decay?
Constant percentage rate?
November 17, 2009
Determine the exponential function with an initial
population = 502,000, increasing at a rate of 1.7% per
year.
November 17, 2009
Radioactive Decay
3. The half-life of carbon-14 is 5730 yrs. If you start with 600 g of
carbon-14, how much do you have left after 34,380 yrs?
November 17, 2009
Determine the exponential function with initial mass =
17g, halving once every 32 hours.
November 17, 2009
Use the 1950-2000 data in Table 3.12 (Pg. 297) to predict
Phoenix's population for 2003. Compare the result listed with
the listed value for 2003. Repeat these steps using
1960-2000 data to create the model.