NEED HELP PLEASE

thanks a lot

2. A record label uses the following function to model the sales of a new release.

a(t)= -90t^2+8100t

The number of albums sold is a function of time, “t”, in days. On which day were the most albums sold? What is the maximum number of albums sold on that day?

## Algebra Problem Solving Help?

March 23rd, 2013 admin

If you differentiat a(t), you should get : da/dt = -180t + 8100

Equating that to 0 will give you the t that you are looking for

That is, -180t + 8100 = 0

solving this, you will get t = 45

So, the most albums were sold on the 45th day

Factor the right side:

a(t) = -90t(t – 90)

Sales will be zero at t = 0, rise to a peak, and fall off to zero again at t = 90. Midway between 0 and 90, sales will peak at t = 45.

The maximum sold will be on day 45.

Substitute 45 for t and solve for a:

a(45) = (-90 * 45^2) + (8100 * 45) = (-90 * 2025) + 364,500 = -182,250 + 364,500 = 182,250

There will be 182,250 albums sold that day.

This is the equation of a parabola, which is symmetrical. Find the two zeros by solving

0 = -90t^2 + 8100t You can solve by factoring. -90t(t – 90) = 0. The two zeros are 0 and 90. The maximum (vertex) of the parabola will be at the t that is exactly in the middle of 0 and 90….so t = 45. Day 45 is the day with most albums sold. substitute 45 for t to find the number of albums sold on that day. -90(2025) + 8100(45)=182250