SOLUTION: ``The record label uses the following function to model the saled 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 w

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Question 677120: ``The record label uses the following function to model the saled 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? I know that the answer is day 45 and 182,250 records. but what work gets me there? I dont know how to get the answer please help! ''.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The most albums are sold on the day in which the quadratic has a maximum value. At the maximum value da/dt = 0:
da/dt = 0 = -180t + 8100
Solving for t gives t = 45 days
The maximum number is a(45) = -90*45^2 + 8100*45 = 182,250
These results can be seen by graphing the function
graph%28300%2C300%2C-100%2C100%2C-10000%2C200000%2C-90%2Ax%5E2%2B8100%2Ax%29