Question

Leander planted 100 acres with soybeans and he plans to increase his field size by 3% each year. Write a model to represent the size of his field (in acres) in any given year.

Answer 1

Let S0 be the initial size of the field at the year y, r the size increase rate per year and t some given year. Then, the size S of the field in the year t is given by;

`S=S_0\cdot(1+r)^(t-y)`

If r = 0.03, S0 = 100 acres, and we set y as 0, we have:

`S=100\cdot1.03^t`

This exponential equation represent the size of the field, in acres, after t years it has been established.