Find the interest earned on an interest-bearing account

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?

Can I assume that you have calculus for this? In order to calculate an average, I would integrate B(t) with respect to t, then divide it by the total time (31 days for July 30 days for November).

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...

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Dear Bella,

July has 31 days, so, if I'm reading the problem correctly

B(t) = (5.5)t^{2} - 300t + 5000

Bella, I'm afraid there might be something wrong with this equation. As written, it predicts that our poor account holder will be losing money. For 0 > t ≤ 54.5455, 300*t will be greater than (5.5)*t^{2} and the $5000 in the account will be diminished. Not until day 55 arrives will the (5.5)t^{2} term be larger than the (300)*t term.

Something doesn't flush her, Bella. Have a look at that original equation again and see if you entered it correctly.

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