Calculate the time needed for a certain bacterial growth

It has been discovered that a population of bacteria grows according to the following law: If there are nt bacteria at time t then one hour later at time t + 1 there will be

where both - alpha and K - are positive numbers that controls the growth rate and defines capacity, respectively.

**Hints:** Remember to import all the packages. You will need to import numpy and math.

**Example:** Starting with n0 = 100 bacteria and setting α = 0.3 and K = 1010, let us find out when the population exceeds N = 500. Running the simulation, we get the following sequence of population sizes.

n0 n1 n2 n3 n4 n5 n6 n7 n8
100 127.03 160.35 200.81 249.08 305.37 369.29 439.56 514.04

In this case, the program should return 8.