1. D IFFERENTIAL E QUATION A PPLICATIONS G ROWTH AND D ECAY 5-G

2. Growth and Decay Model If y is a differentiable function of t, such that y > 0 and for some constant k then Rate of change of the variable is proportional to the variable itself.

3. 1) If and

4. Growth and Decay Model C is the initial value (the amount present at time t = 0 k is the constant of proportionality ( k > 0 growth and k < 0 for decay) t is time Y is the amount present at time t.

5. Interest Compounded Continuously P is the initial value (the principal amount present at time t = 0) r is the interest rate ( expressed as a decimal) t is time A is the amount present at time t.

6. 2) What is the rate of growth of the population of a city whose population triples every 100 years?

7. 3) If the initial population of bacteria is 1500 and the population quadrupled during the first two days. What is the population after 3 days?

8. 4) The rate of decay of a radioactive substance is proportional to the amount present. Four years ago there were 12 grams of substance. Now there are 8 grams. How many grams will there be 8 years from now?

9. 5) Find the principal, P, that must be invested at a rate of 7% APR compounded continuously so the $500,000 will be available in 20 years.

10. 6) Let y represent the mass, in pounds, of a radioactive element whose half- life is 4000 years. If there are 200 pounds of the element in an inactive mine, how much will still remain in 1000 years?

11. 7) A certain population increase at a rate proportional to the square root of the population. If the population goes from 2500 to 3600 in five years, what is the population at the end of t years?

12. H OME W ORK Growth and Decay Worksheet 5-G