Question

An ice cream store's summer revenue is approximated by f open parentheses t close parentheses equals 300 plus 4.5 t minus 0.05 space t squared dollars perday for 0 less or equal than t less or equal than 92 , where t is measured in days after June 1. Suppose this ice cream store deposits its receipts in an account paying 5% interest per year compounded continuously. How much money will it have in the account at the end of August? (Hint: 1. the end of August is 92 days after June 1. 2. In the formula F V equals integral subscript a superscript b f open parentheses t close parentheses e to the power of r open parentheses b minus t close parentheses end exponent d t , the unit of time t can be day or years, but generally the r is the yearly rate, the value of left parenthesis b minus t right parenthesis should be in the unit of year. So when t is in the unit of day, the formula of future value is F V equals integral subscript a superscript b f open parentheses t close parentheses e to the power of r asterisk times fraction numerator b minus t over denominator 365 end fraction end exponent d t .

Answer 1

The future value of all of this money at the end of the 92nd day, at the end of August was obtained to be $3,260,336.48

Explanation:

The complete question is attached to this solution

From the question,

The revenue per day is given as

f(t) = 300 + 4.5t - 0.05t² for 0≤t≤92

The future value is also given in the question. Note that this figure value is compounded over day 0 to 92.

So, a = 0, b = 92, r = 1.05

This integral is evaluated and presented in the attached images to this question.

The integral is evaluated on the second, third and fourth attached images to this solution.

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