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

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Presentation transcript:

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

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.

1) If and

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.

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.

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

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?

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?

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.

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?

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?

H OME W ORK Growth and Decay Worksheet 5-G