Given:
In 2010, cornfield farms produced 175,000 bushels of corn. Each year since 2010, their total corn harvest has increased by 2.5% over the previous year.
Required:
Write the exponential function f(x) that models the number of bushels of corn produced x years after 2010.
Explanation:
The exponential growth is given by the formula:
[tex]f(x)=P(1+\frac{r}{100})^t[/tex]
Where P = initial amount
r = rate of interest
t = time in years.
Thus the exponential growth is:
[tex]\begin{gathered} f(x)=175,000(1+\frac{2.5}{100})^x \\ f(x)=175,000(1+0.025)^x \\ f(x)=175,000(1.025)^x \end{gathered}[/tex]
Final Answer:
The exponential growth function is:
[tex]f(x)=175,000(1.025)^x[/tex]
