Every month, a particular interest-bearing account earns 0.2 percent interest on the average balance for that month. The function B(t) =7.5t^2 -300t +5000 represents one investor's balance in this account during the month of November. B(t) gives the number of dollars in the account on day t, with t=0 being the beginning of the first day. How much interest will the account earn this month?
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The average value of a function f(t) on an interval [a,b] is given by
∫ab f(t) dt /(b-a).
In your case, the average of B(t)=7.5t2-300t+500 on [0,30] is given by
∫030 B(t) dt /30 = 2750.
0.2% interest on this balance is 2750*0.002 = $5.5.