Question

A farmer sells corn that he grows in a square field. Each side of the field is 40 meters long, and he plans to extend the side lengths by 3 meters each year so he can plant more corn. How can the farmer use this information to calculate the area of the field, A, after t years?

Answer 1

The farmer can calculate the area of the field after t years by using the formula A = (40 + 3t)², which accounts for the annual increase in each side's length. This results in A = 1600 + 120t + 9t² square meters.

Step-by-step explanation:

To calculate the area, A, of the farmer's square field after t years, we need to account for the annual extension of each side by 3 meters. Initially, each side of the field is 40 meters. After t years, each side will be (40 + 3t) meters long. The formula for the area of a square is side length squared, so:

A = (side length) · (side length)

Therefore, the area of the field after t years is:

A = (40 + 3t)² = (40 + 3t) · (40 + 3t)

Expanding this, we have:

A = 1600 + 120t + 9t² square meters

This quadratic equation represents the growing area of the field in square meters as a function of time, t, in years.

Answer 2

3+3=6

6 meters per year

6t+A