For Loops

Exponential Growth 1

The field of population biology is interested in how the number of individuals (N) of a population (all members of a species living in some region) changes through time. The most basic model in population biology is exponential growth, which simply says that each individual reproduces at a constant rate. Therefore the number of individuals at time t + 1 is equal to the number of individuals at time t times the per individual rate of reproduction (r). In other words N(t+1) = N(t) + r*N(t).

One of your lab mates is conducting an experiment to determine if the growth of insect populations follows exponential growth. They are really good at cultivating insect populations, but they can barely turn their computer on let alone program with it, so they have come to you for help in generating the predicted population sizes for their experiments. The first experiment will measure the population sizes of a species with a reproductive rate of 0.152 at 10 weeks, 50 weeks and 100 weeks. The experiment will start with an initial population size of 10 individuals.

Since you know there will be more experiments later, write a function, get_pop_size_at_t(init_pop_size, reprod_rate, time_of_sample), that returns the population size of a species undergoing exponential growth at the time_of_sample when the population begins at init_pop_size individuals when t = 0. Use this function to determine the expected population size at each of the specified points in time and print the results to the screen.