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Math Help - exponential growth/decay word problem

  1. #1
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    exponential growth/decay word problem

    The department of health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing exponentially at an annual rate of 9%. The first year that statistics were collected, 5000 cases were reported.

    a. Estimate the # of cases reported after 7 years.

    b. Estimate the # of years, to the nearest tenth, required for the # of reported cases to rise to 11,000.
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    Quote Originally Posted by cityismine View Post
    The department of health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing exponentially at an annual rate of 9%. The first year that statistics were collected, 5000 cases were reported.

    a. Estimate the # of cases reported after 7 years.

    b. Estimate the # of years, to the nearest tenth, required for the # of reported cases to rise to 11,000.
    a) A = (5000) \left( 1 + \frac{9}{100} \right) ^{7}

    b) 11 000 = (5000) \left( 1 + \frac{9}{100} \right) ^{n}

    n = \log_{(5000) \left( 1 + \frac{9}{100} \right)} 11000
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