Module 3 Discussion Question - Discussion Board Group 7
From MAT151 22224
Answer the following questions. Be sure to show all work and explain where helpful. Do not forget to respond to at least two classmates.
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.
A. Identify the input quantity of the function.
B. Identify the output quantity of the function.
C. 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.)
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 $P = g^{-1}(c)$.
H. Evaluate $g^{-1}(12)$.
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