Now, consider a matrix C = 0 1 1 0 . Interpret this matrix as a Markov chain for two states "sunny" and "rainy". What is the long-term dynamic if we start from a "sunny" state?

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.

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