A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the...

  

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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 $10.04. However, the price per box was $24.32 when 80% of the crop was frozen. A. Identify the input quantity of the function and identify the output quantity of the function. B. Identify the constant rate of change needed to model the linear equation. Include units! C. 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: Do not simplify. Your equation should NOT be in y=mx+b form.) D. Identify a Practical Domain for the function and explain your reasoning for the choice. E. Identify a Practical Range for the function and explain your reasoning for the choice. F. Explain the meaning of g-1 (12) in the context of the problem. G. Determine the inverse formula for P = g-¹ (c). -1 H. Evaluate g¹ (12). 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 $10.04. However, the price per box was $24.32 when 80% of the crop was frozen. A. Identify the input quantity of the function and identify the output quantity of the function. B. Identify the constant rate of change needed to model the linear equation. Include units! C. 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: Do not simplify. Your equation should NOT be in y=mx+b form.) D. Identify a Practical Domain for the function and explain your reasoning for the choice. E. Identify a Practical Range for the function and explain your reasoning for the choice. F. Explain the meaning of g-1 (12) in the context of the problem. G. Determine the inverse formula for P = g-¹ (c). -1 H. Evaluate g¹ (12).

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