A company's daily profit is modeled by the function P(x) = 3x - 50, where x represents the… — ACT

A company's daily profit is modeled by the function $P(x) = 3x - 50$ , where $x$ represents the number of items sold. The number of items sold depends on the number of hours the store is open, $h$ , according to the function $x(h) = 5h$ . What is the daily profit, in dollars, when the store is open for $8$ hours?

A
-26
B
40
70Answer
D
120
E
170

Answer

Evaluating the composite function in the correct order,

P(x(8))

, yields

70

. First, find the number of items sold when the store is open for 8 hours:

x(8) = 5(8) = 40

. Then, calculate the daily profit by substituting this output into the profit function:

P(40) = 3(40) - 50 = 120 - 50 = 70

Step-by-Step Solution

Determine the number of items sold,

x

, when the store is open for

8

hours by evaluating the function

x(h) = 5h

h = 8

x(8) = 5 \times 8 = 40

items.

The number of items sold is the input for the profit function.

Substitute the number of items sold (

x = 40

) into the profit function

P(x) = 3x - 50

P(40) = 3(40) - 50 = 120 - 50 = 70

dollars.

Evaluating the profit function at the given number of items sold determines the final daily profit.

Key Concept

Evaluating a composite function by finding the output of the inner function and using it as the input for the outer function.

Estimated Time:1m 0s

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