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Math Help - another exponential world problem

  1. #1
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    another exponential world problem

    The accompanying table shows the number of milligrams, y, of a dose of a cold medication that remains in the body x hours after the dose has been ingested.

    x(hrs) 2, 3, 5, 7, 9
    y(mg) 11, 6.7, 2.9, 1.5, 0.9

    Determine an exponential function y=ax^b that best fits the given data. Then estimate constants a and b to the nearest tenth. Find to the nearest minute when the amount of the drug that remains in the body first falls below 0.5 milligram.
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    Quote Originally Posted by cityismine View Post
    The accompanying table shows the number of milligrams, y, of a dose of a cold medication that remains in the body x hours after the dose has been ingested.

    x(hrs) 2, 3, 5, 7, 9
    y(mg) 11, 6.7, 2.9, 1.5, 0.9

    Determine an exponential function y=ax^b that best fits the given data. Then estimate constants a and b to the nearest tenth. Find to the nearest minute when the amount of the drug that remains in the body first falls below 0.5 milligram.
    My advice:

    y = ax^b

    ln(y) = ln(ax^b)

    ln(y) = b \cdot ln(x) + ln(a)

    So if you plot ln(y) vs. ln(x) you will get a line. Do a best fit regression on the ln(y) vs. ln(x) data and the slope will be b and the intercept ln(a).

    -Dan
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