Let P(t) be the population (in hundreds) of a group of wolverines occupying a no

Question

Let P(t) be the population (in hundreds) of a group of wolverines occupying a northwest forest t years after 2000. Suppose that P(t) satisfies the differential equation P'(t) = 0.3 P(t), P(0) = 5. For all parts below, enter symbolic (exact value expression) answers rather than numeric answers. (a) Find the formula for P(t): (b) What was the initial population? (c) What is the growth constant? k= (d) How large is the population after 3 years? wolverines (e) How quickly is the population growing after 3 years? wolverines per year

Explanation / Answer

Hi,

a) Since P' - .3P = 0

The solution is P = Ae^(.3t)

Since P(0)=5

P = 5e^(.3t)

b) Initial pop is where t=0 so 5 hundred wolverines

c) The growth constant is 0.3

d) P(3) = 5e^(0.3*3) = 12.3, so 12 wolverines (and a prego one!)

e) Take the derivative

P'(x)= 1.5e^(0.3t)

P(3)= 3.7

So 370 wolv/yr

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