Rocio predicts that the amount of corn, C. in bushels, produced on her farm t years from now can be modeled

by the function Cl (t) = 80t + 1000, while the price, P, in dollars, per bushel of corn t years from now can be

modeled by the function P (t) = 0.03t + 5.

Question:

Rocio predicts that the amount of corn, C. in bushels, produced on her farm t years from now can be modeled

by the function C (t) = 80t + 1000, while the price, P, in dollars, per bushel of corn t years from now can be

modeled by the function P (t) = 0.03t + 5. Let I be Rocio's predicted total income from producing corn t years from now.

Answer: I (t) = 2.4t^2 + 430t + 5000

Step-by-step explanation:

Given that:

Amount of corn sold in t years is modeled by:

C (t) = 80t + 1000

Price of corn sold in t years is modeled by:

P (t) = 0.03t + 5

Therefore, total income = (amount sold in brushels in t years * price in dollar per bushel I. t years)

Therefore, I (t) = C (t) * P (t)

I (t) = (80t + 1000) * (0.03t + 5)

I (t) = 2.4t^2 + 400t + 30t + 5000

I (t) = 2.4t^2 + 430t + 5000