- #1

Naeem

- 194

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a) Determine the population size P as a function of days t.

We know,

P(0) = 100

P(1) = 200

P max = 10,000

Logisitc equation:

dP/dt = kP ( 1-P/Pmax)

Integrating both sides:

Integral ( dP/P(1-P/m) = Integral kdt

Using Partial fractions, we get:

PMax - P^2 = Ce^kt

Therefore,

C = PM - P^2 / e^kt

P(t) = Ce^kt / Pmax - P

Is this correct,

b. How many flies are present after 3 days?

For, this we can find C, using the initial condition: P(0) = 100

To find k, we can use P(1) = 200, and Pmax = 10,000

After finding all this,

We can do, P(3) = Ce^kt / Pmax - P

Any suggestions / ideas, Please help