Algebra Problem Solving Help?

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?

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3 Responses to “Algebra Problem Solving Help?”

  1. Frank says:

    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

  2. Bob B says:

    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.

  3. Carmel says:

    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

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