If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply?

At $100 per unit, q is:

q = 0.2(100)^2 + 9(100) = (0.2 * 10000) + 900 = 2000 + 900 = 2900

The rate of change is found with the first derivative:

q' = 0.4p + 9

With p decreasing at $1 per week, using w for the number of weeks:

q' = 0.4(-1) + 9 = -0.4w + 9

The quantity will drop to zero when 0.4 times the number of weeks reaches 9:

0.4w = 9

w = 9 / 0.4 = 22.5 weeks

The quantity will drop to zero over the next 22.5 weeks.

without any computation you can see that they have a direct relationship between the price and the quantity therefore it will decrease the quantity every week but its not clear when it asks how it will affect the quantity the quantity will decrease every week as well but the question needs to be a little clearer if you plot this function using excel you can see that q decreases every week as a matter of fact by week 50 that is when the price is gone down to $50 you will find that the quantity goes down from 2900 to only 950

Seriously Dude... Seriously.

Insert $100 in for p... to get q.

Then insert say $90 and see what happens to q.