The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55? The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.

The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.

The profit function is given as:

Calculate P(x), when x = 50.

So, we have:

Calculate P(x), when x = 55.

So, we have:

The average rate of change from x = 50, to 55 is then calculated using:

So, we have:

Divide

The function is in 1000 units.

So, we have:

-375 implies a decrease of $375 for every $1 increase in sales

Hence, the correct statement is (b)

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The profit decreases by $ 375 for every $ 1 increase in the selling price.

Step-by-step explanation:

From the definition of the secant line we get that the average rate of change of , where is the selling price of the product, measured in dollars per unit, is:

(1)

Now we evaluate the function at each bound:

x = 50

x = 55

Then, the average rate of change is:

Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)

do your own work and don"t cheat.

step-by-step explanation: