Question 986824: Suppose a devastating freeze destroyed roughly 65% of California Central Valley's orange crop. As a result of the freeze, an orange that cost $0.50 before the freeze would cost $1.50 after the freeze. Model the price c of an orange as a linear function of the percentage p of the crop that was destroyed. (Hint: When 0% of the crop was destroyed, the price was $0.50.)
(a) Determine the vertical and horizontal intercepts of the graph of the implied linear function algebraically.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose a devastating freeze destroyed roughly 65% of California Central Valley's orange crop. As a result of the freeze, an orange that cost $0.50 before the freeze would cost $1.50 after the freeze. Model the price c of an orange as a linear function of the percentage p of the crop that was destroyed. (Hint: When 0% of the crop was destroyed, the price was $0.50.)
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You have 2 points relating percent of damage and price:: (0,50),(65,150)
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Form:: P = mD + b where P is price and D is percent of damage.
slope = (150-50)/(65-0) = 100/65 = 20/13
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Price when D is zero = 50
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Equation:
P = (20/13)D + 50
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(a) Determine the vertical and horizontal intercepts of the graph of the implied linear function algebraically.
Vertical intercept:: Let D = 0, then Price = 50
Horizontal intercept:: Let Price = 0, then D = -50*13/20 = -(5/2)13
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Cheers,
Stan H.
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