Question

Suppose that the number of paramecia in a petri dish P(t) is 100 at time t = 0 and 250 at time t = 1, where t
is in hours. The carrying capacity of the petri dish is 2000 paramecia. Use Euler’s method with step size 0.5 to
estimate how many paramecia there will be at time t = 3. (Hint. Use the logistic model. Since P(0) and P(1)
are significantly less than the carrying capacity of the petri dish, assume that the growth of P(t) from t = 0 to
t = 1 follows the linear model dP=dt = kP and use this assumption to estimate the growth rate k.)

Answer 1

anyone?

Answer 2

I'm not sure what they mean by the logistic model, but here is how I would solve it.

Okay, so Euler's method is y(n+1) = y(n) + h*f(tn, yn). First step is to find f(to, yo). Because it is given when t = 0, it's just going to be equal to yo so 100. From there, you plug and chug.
y1 = 100 + 0.5 * 100
y2 = y1 + 0.5 * f(y1)
y3 = y2 + 0.5 *f(y2)
etc...

You would just continue until you hit your three minutes. I got approximately 1140 using this method.