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14 May, 23:31

A certain first covers an area of 4100 km^2. Each year this area decreases by 3.75 percent. What will the area be after 11 years?

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  1. 15 May, 00:51
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    The formula to use is

    A = P (1+r) ^t

    where,

    A = final amount after t years

    P = initial amount = 4100

    r = rate of increase or decay = - 3.75% = - 3.75/100 = - 0.0375

    t = number of years = 11

    The value of r is negative to indicate exponential decay. Also notice that I divided by 100 to convert from - 3.75% to - 0.0375

    Using those values, we plug them into the formula to get,

    A = P (1+r) ^t

    A = 4100 (1 + (-0.0375)) ^11

    A = 4100 (1-0.0375) ^11

    A = 4100 (0.9625) ^11

    A = 4100*0.65676215615721

    A = 2692.72484024457

    A = 2693

    Rounding to the nearest whole number, the answer is approximately 2693 km^2.
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