Logistic Derivative at Point

Problem

The logistic solution is y(t) = k / (1 + ((k - y0) / y0) * e^(-r*t)). Its rate of change is y'(t) = r * y(t) * (1 - y(t) / k).

Given t, the initial population y0 > 0, the rate r, and the carrying capacity k, compute y(t) and return the derivative at that time.

Hint

First evaluate the closed-form population, then plug it into the logistic rate law.

case 1

in: [0,10,1,100]

expected: 9

case 2

in: [10,10,1,100]

expected: 0.04082656655153957

case 3

in: [1,50,1,100]

expected: 19.66119332414819

case 4

in: [0,4,0.5,8]

expected: 1

Starter codePython

def logistic_derivative(t, y0, r, k):
    # Your code here
    pass

4 test cases · run your code against them in the editor