A devastating freeze in California’s Central Valley in January 2007 wiped out approximately 75% of the state’s citrus crop. It turns out that the cost for a box of oranges is a function of the percentage of the citrus crop that was frozen, i. e. c=g(P) , where c is the price of a box of oranges and P is the percentage of the citrus crop that was frozen. When only 20% of the crop was frozen, the price for a box of oranges was $11.58. However, the price per box was $25.32 when 80% of the crop was frozen. Identify the input quantity of the function.
Identify the output quantity of the function.
Using the method demonstrated in the Module 3 presentation, create a formula for a linear function that represents this situation. i. e. your formula should use one of the given reference points rather than the vertical intercept. (Note: You will need to first find the constant rate of change.)
Identify a Practical Domain for the function and explain your reasoning for the choice.
Identify a Practical Range for the function and explain your reasoning for the choice.
Explain the meaning of g−1(12) in the context of the problem.
Determine the inverse formula for P=g−1(c) .
Evaluate g−1(12) .