A profit formula for dining plates from the previous year was modeled by the function P(d) = –15d2 + 1,200d – 2,000. The manufacturer noticed an increase in the number of units sold by 50% the next year, which can be modeled by the function l(d) = 1.5d.
Answer
A
P(d) = –7.5d2 + 600d – 2,000
B
P(d) = –3.75d2 + 600d – 2,000
C
P(d) = –22.5d2 + 1,800d – 2,000
D
P(d) = –33.75d2 + 1,800d – 2,000
Explanation
An increase of 50% means the new number of units is 1.5d, so substitute 1.5d for d in the original profit formula. This gives P(1.5d) = −15(1.5d)² + 1,200(1.5d) − 2,000 = −33.75d² + 1,800d − 2,000. The matching choice is D.
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