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Math Help - Can I get help on a rate of change problem?

  1. #1
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    Can I get help on a rate of change problem?

    The rate of change in a person's body temp, with respect to the dosage of X milligrams of a drug, is given by D Prime of x=  \frac{7}{x+5} One milligram raises the body temp 2.3* C. Find the function

    Where do I start with this problem?



    Thanks
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  2. #2
    MHF Contributor Calculus26's Avatar
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    D ' (x) = 7/(x+5)

    D(x) = 7ln(x+5) + C

    taking the normal body temp to be 37.5 (Centigrade) then D(1) = 39.8

    D(1) = 7ln(6) + C = 39.8 which yields C= 39.8 - 7ln(6)

    D(x) = 7ln(x+5) + 39.8 - 7ln(6)
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  3. #3
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    Is the answer D(x)= 7ln|x+5|+2.3, or D(x)= 7ln|x+5|-10.2?

    Those are the 2 multiple choose answers that are given with this problem?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    If D(x) represents the persons body temperature neither one is right

    as D(0) = 13.6 deg in one case and 1 deg in the other--in either case

    the patient is long dead.

    If D(x) represents the temp above normal body temp

    D(x) = 7ln(x+5) + C

    D(1) = 7ln(6) +C = 2.3

    in which case C = -10.2

    D(x) = 7ln(x+5) - 10.2
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