Question

Jodie has an orange grove. She noticed that if 27 trees are planted per acre, each tree produces about 568 oranges per year. For each additional orange tree planted per acre, each tree produces 12 less oranges per year. Which equation could Jodie use to give her the amount of oranges her trees produce per year, F, as a function of the number of trees over 27, t?
A. -12t2 + 244t + 15,336 = F
B. 12t2 - 244t - 15,336 = F
C. 568t = F
D. 568t - 12 = F

Answer 1

The correct answer is Choice A.

There are two parts to determining the total number of oranges that her trees produces. We have to multiply the number of trees by the number of oranges per tree.

It starts as:  27 x 568

However, we are adding a new tree and that decreases the amount of apples per tree by 12. If we let the number of new trees equal t, then we could write the following function.

f(t) = (27 + t)(568 - 12t)  because the trees go up by 1 and the overall production goes down by 12 per t.

If you FOIL out that equation, you will have Choice A.