How do I create exponential equations?

Question

A colonial settlement started with 500 people and food sources adequate to feed 500 people. They are able to expand their resources to feed 30 additional people each year. The population is growing at 5% per year.

1. Create an equation that models the number of people that can be fed in a given year. 

2.Create an equation that models the number of people, the population, in a given year. 

Answer 1

For the growth of the food valuable it is simply a linear growth. F=500+30t

For the population it grows 5% per year. We are assuming a continuous growth, therefore we use the equation P=P_0e^(rt) which is derived originally for continuous compound interest. P=500e^(0.05*t)

where t is measured in years.