Question

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.

Answer 1

Answer:

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 $P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5$, where $x$ is the selling price of the product, measured in dollars per unit, is:

$r = \frac{P(55)-P(50)}{55-50}$ (1)

Now we evaluate the function at each bound:

x = 50

$P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5$

$P(50) = 11$

x = 55

$P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5$

$P(55) = 9.125$

Then, the average rate of change is:

$r = \frac{9.125-11}{55-50}$

$r = -0.375$

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