100 points The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company:

Graph of quadratic function f of x having x intercepts at ordered pairs negative 0, 0 and 10, 0. The vertex is at 5, 160.
(Picture attached)

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent?

Part C: Describe the constraints of the domain.

A.

intercepts: prices at which profit is zero

maximum: price at which profit is maximum

increasing: x < 5, where increasing price means increasing profit

decreasing: 5 < x, where increasing price means decreasing profit

 B. 20 dollars per dollar, the rate of increase of profit with respect to price changes

 C. 0 ≤ x ≤10

Part A: The description of the graph tells you that each point on the graph represents (price, profit). So, x-intercept points that are (price, 0) represent prices at which profit is zero. The point (price, maximum) = (5, 160) represents the price at which profit is maximized.

The curve is increasing to the left of the maximum, on the interval x < 5, and is decreasing to the right of the maximum, on the interval 5 < x. These are the intervals where increasing prices result in increasing and decreasing profits, respectively.

Part B:

The average rate of change between (2, 100) and (5, 160) is given by the slope formula:

 m = (y2 -y1)/(x2 -x1) = (160 -100)/(5 -2) = 60/3 = 20 . . . . dollars per dollar

On average company profit increases by $20 for each $1 increase in the price of its pencils.

Part C:

Prices are not usually negative, so the domain is likely constrained to 0 ≤ x. The price could be set high enough to result in negative profit, but that is not a practical choice. So, the upper end of the reasonable domain is x ≤ 10.

The reasonable constraints on the domain are those than ensure profit is non-negative: 0 ≤ x ≤ 10.

Step-by-step explanation:

Hope this helps:)

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

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