Question

Hiw to write an exponential function that models the number of bushels of corn produced x years after 2010

Answer 1

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.

Step-by-step explanation:

The exponential growth is given by the formula:

`f(x)=P(1+(r)/(100))^t`

Where P = initial amount

r = rate of interest

t = time in years.

Thus the exponential growth is:

`\begin{gathered} f(x)=175,000(1+(2.5)/(100))^x \\ f(x)=175,000(1+0.025)^x \\ f(x)=175,000(1.025)^x \end{gathered}`

Final Answer:

The exponential growth function is:

`f(x)=175,000(1.025)^x`