If all goes according to plan, the function A(t)=200(1.1)^(t) will model the amount of potatoes, A, in bushels, produced by Burian's farm t years from now, and the function R(t)=5000(1.111)^(t) will model the revenue, R, in dollars, earned from selling these potatoes. Let P be the proposed price of a single bushel of potatoes t years from now. Write a formula for P(t) in terms of A(t) and R(t). P(t)= Write a formula for P(t) in terms of t. P(t)=

Question

If all goes according to plan, the function  A(t)=200(1.1)^(t) will model the amount of potatoes,  A, in bushels, produced by Burian's farm  t years from now, and the function  R(t)=5000(1.111)^(t) will model the revenue,  R, in dollars, earned from selling these potatoes. Let  P be the proposed price of a single bushel of potatoes  t years from now. Write a formula for  P(t) in terms of  A(t) and  R(t).  P(t)= Write a formula for  P(t) in terms of  t.  P(t)=

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Understand Relationship: Understand the relationship between the amount of potatoes produced, the revenue earned, and the price per bushel. The price per bushel of potatoes, P(t), is the revenue earned, R(t), divided by the amount of potatoes produced, A(t). P(t) = R(t) / A(t)Substitute Given Functions: Substitute the given functions for A(t) and R(t) into the formula for P(t). A(t) = 200(1.1)^t R(t) = 5000(1.111)^t P(t) = R(t) / A(t) = 5000(1.111)^t / 200(1.1)^tSimplify Formula: Simplify the formula for P(t) by dividing the coefficients and the exponential terms separately. P(t) = (5000 / 200) * ((1.111)^t / (1.1)^t) P(t) = 25 * (1.111/1.1)^tCalculate Base: Calculate the base of the exponential term in the simplified formula for P(t). (1.111 / 1.1) = 1.01 P(t) = 25 * (1.01)^t

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