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:
[tex]y=100*(1+0.03)^x[/tex]We will find the number of years (x) required to reach y = 250 acres
so, substitute y = 250 and then solve for x:
[tex]\begin{gathered} 250=100*(1+0.03)^x \\ \\ 100(1.03)^x=250 \\ \\ 1.03^x=\frac{250}{100}=2.5 \\ \\ x*ln1.03=ln2.5 \\ \\ x=\frac{ln2.5}{ln1.03}=30.9989\approx31 \end{gathered}[/tex]So, the answer will be the number of years = 31
