Logistic Growth Value

Problem

The logistic model has the closed-form solution y(t) = K / (1 + ((K - y0) / y0) * e^(-r*t)), where K is the carrying capacity and r the growth rate.

Given t, initial population y0 > 0, capacity k, and rate r, return y(t).

Hint

At t = 0 the exponential equals 1, so y = y0; large t drives y toward K.

case 1

in: [0,10,100,1]

expected: 10

case 2

in: [10,100,100,1]

expected: 100

case 3

in: [1,10,100,1]

expected: 23.19693166840739

case 4

in: [5,50,100,0.5]

expected: 92.41418199787564

Starter codePython

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

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