1. Clicker Question 1
A population of geese grows exponentially, starting with 50 individuals, at a continuous rate of 7% per year. How long will it take for the population to reach 150 geese?
A. 8.3 years
B years
C years
D years
E. It will never reach 150

2. Clicker Question 2
A population of geese grows exponentially, starting with 50 individuals, at a continuous rate of 7% per year. At what rate (in geese/year) is the population growing after 5 years?
A. 1 goose/year
B. 5 geese/year
C. 7 geese/year
D. 10 geese/year
E. 12 geese/year

3. More on Exponential Growth and Decay (2/10/12)
In the equation P (t) = C e k t , there are two “parameters”: C (the initial amount) and k (the relative or continuous growth rate – note that if k is positive we have growth and if it is negative we have decay).
C is always given. k may be given explicitly; or it may not be given, but one additional data point is given. From this, k can be computed.

4. An example
A population of mice starts with 100 individuals and grows exponentially. After 3 months, the population is 130.
What is the continuous growth rate k ?
How big is the population after 10 months?
What is the rate of change (in mice/month) after 10 months?

5. Clicker Question 3
My back account, which started with $5000, is dwindling exponentially. After 6 months, it was down to $4500. What is the approximate continuous growth rate k (time measured in months)?
A. 10.5% B %
C. 1.76% D %
E %

6. Example: Radioactive Decay
The half-life of a radioactive substance is the number of years for half the substance to decay.
Here we compute k via the equation ½ = ek (the half-life) . (Why??)
The half-life of radium-226 is 1590 years.
If I start with 100 mg, how much is there after 200 years?
How long before only 20 mg are left?

7. Assignment for Monday
Do Exercises 3 (repeat from last time), 5a, and 9 on page 243.