The demand function for a certain product, p=d(q), is linear, where p is the price per item in dollars and q is the quantity demanded. if p increases by 8$, market research shows that q drops by two items. in addition, 50 items are purchased if the price is 250. find a formula for q as a function

Step-by-step explanation:

Given:

is a linear model for demand function

where represents the price per item in dollars and  is the quantity demanded.

With increase in by $8 there is a decrease in by 2 items.

For items purchased the price .

To find   as a function of which is  

Since its a linear model, so we can find rate of change or slope of line from the given data.

Slope

So, the function can be written as:

where is the initial value or the y-intercept.

Using the point

Adding 62.5 both sides.

∴

So,

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half