document.write( "Question 677120: ``The record label uses the following function to model the saled of a new release.
\n" ); document.write( "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! ''. \n" ); document.write( "

Algebra.Com's Answer #420701 by htmentor(1343) $\"\"$ $\"About$

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:
\n" ); document.write( "da/dt = 0 = -180t + 8100
\n" ); document.write( "Solving for t gives t = 45 days
\n" ); document.write( "The maximum number is a(45) = -90*45^2 + 8100*45 = 182,250
\n" ); document.write( "These results can be seen by graphing the function
\n" ); document.write( " $\"graph%28300%2C300%2C-100%2C100%2C-10000%2C200000%2C-90%2Ax%5E2%2B8100%2Ax%29\"$ \n" ); document.write( "

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