A hair-styling salon charges $11.00 for a haircut, and an average of 75 people stop in for haircuts each day. The owner is thinking of increasing the price, and he estimates that every time he raises the price of a haircut by $1.00, the number of people coming in for haircuts will decrease by 3 per day. Write the function that represents the estimated revenue per day from haircuts as a function of the number of dollars the price of a haircut is raised?

Question

anonymous · Answer

can someone help me with this?

anonymous · Answer

We have two variables, the number of customers and the price of the haircut. The number of customers is dependent on the price, so let that be y and the price be the independent variable, x.

So then we can say a point on the function is (11, 75).

The change in customers with price is proportional, so that means the function is linear. Slope = rise/run = Δy/Δx = change in customers/change in price = -3/1 = -3.

So your function will be the line through (11, 75) with the slope -3.

anonymous · Answer

You can use point-slope equation for a line to come up with the function and then write it in the format of your choosing.
$$y-y_1=m(x-x_1)$$

anonymous · Answer

thank you so much for the explanation! which of the following would be correct?
r(d) = (11 – d)(75 – 3d)
r(d) = (11 + d)(75 – 3d)

anonymous · Answer

so I guess it's not linear.
11 + d because it's adding dollars, so the 2nd one

anonymous · Answer

so here i've listed all the possibilities, but since the slope is a -3, i would say it would be the last two, i'm just a bit unclear of which one it should be.
r(d) = (11 – d)(75 + 3d)
r(d) = (11 + d)(75 + 3d)
r(d) = (11 + d)(75 – 3d)
r(d) = (11 – d)(75 – 3d)	
@peachpi

anonymous · Answer

yes that is correct. (11 + d)(75 - 3d)