When interest is compounded, the interest earned is added to the principal amount so that it may also earn interest. For a 1-year period, the principal amount Q is given by:

where i is the annual interest rate (given as a decimal) and n is the number of times during the year that the interest is compounded. To lure depositors, banks offer to compound interest at different intervals: semiannually, quarterly, or daily. A certain bank advertises that it compounds interest continuously. If $100 is deposited initially, formulate a mathematical model describing the growth of the initial deposit during the first year. Assume an annual interest rate of 10%.

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