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This is a follow up to the Exponential Growth problem.

In addition to wanting to be able to calculate the predicted abundance at a given point in time for an exponentially growing species, your lab mate is also interested in how long it will take for a species to double in size as a function of it’s growth rate. Write a function that takes the growth rate and initial population size as inputs and returns the number of time steps that it took for the population to double (it’s OK if the population has more than doubled, we just want the time step at which it becomes greater than or equal to twice the starting value). Print the results to the screen for species with growth rates of 0.0001, 0.005, and 0.21, all with initial population sizes of 1000 individuals.

Optional: If you’re feeling clever, try thinking about whether or not the time it takes for a population to double depends on the initial population size. You can play around with this using your function. Based on either your understanding of the math or the results from your computational experiments. Modify your function to be simpler than the one you initially wrote.