Question

Leander planted 100 acres with soybeans and he plans to increase his field size by 3% each year. If Leander wants to stop growing his farm after he hits 250 acres, after how many years will he have to stop increasing the size of his field?

Answer 1

Given:

Leander planted 100 acres with soybeans and he plans to increase his field size by 3% each year.

Let the total planted acres = y, and the number of years = x

The initial planted acres = 100

the rate of increase the planted acres = 3% = 0.03

So, the relation between x and y will be as follows:

`y=100*(1+0.03)^x`

We will find the number of years (x) required to reach y = 250 acres

so, substitute y = 250 and then solve for x:

`\begin{gathered} 250=100*(1+0.03)^x \\ \\ 100(1.03)^x=250 \\ \\ 1.03^x=(250)/(100)=2.5 \\ \\ x*ln1.03=ln2.5 \\ \\ x=(ln2.5)/(ln1.03)=30.9989\approx31 \end{gathered}`

So, the answer will be the number of years = 31