19
QuizMultiple Choice

Modeling Using Function Notation — Quiz

Question 19 • Algebraic Reasoning

A profit formula for dining plates from the previous year was modeled by the function cap p times d is equal to negative 15 d squared plus 1 comma 200 d minus 2 comma 000 The manufacturer noticed an increase in the number of units sold by 50 percent the next year, which can be modeled by the function l times d is equal to 1 point 5 d Which composite function can be used to find the new profit formula after the increase in the number of units?

Answer
A
cap p times open paren l times d close paren is equal to negative 3 point 7 5 d squared plus 600 d minus 2 comma 000
B
cap p times open paren l times d close paren is equal to negative 33 point 7 5 d squared plus 1 comma 800 d minus 2 comma 000
C
cap p times open paren l times d close paren is equal to negative 22 point 5 d squared plus 1 comma 800 d minus 2 comma 000
D
cap p times open paren l times d close paren is equal to negative 7 point 5 d squared plus 600 d minus 2 comma 000

Explanation

To find the new profit, substitute the increased sales amount, l(d) = 1.5d, into the original profit function: p(l(d)) = -15(1.5d)² + 1,200(1.5d) - 2,000. Since (1.5d)² = 2.25d², this simplifies to -33.75d² + 1,800d - 2,000. The correct choice is B.

AI-written and checked against the verified answer.

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