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. 12.2 years C. 15.7 years D. 20.2 years E. It will never reach 150

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

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.

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?

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. -10.5% C. 1.76% D. -1.76% E. -0.76%

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?

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