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Math Help - check my work please

  1. #1
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    check my work please

    The mass of a human liver scales allometrically as ML = 0.082 x MB^0.87, where MB is the individual's body mass. Suppose the body mass of an individual increases by 30%. What is the percent increase in the mass of their liver?

    here's my work..using a person who was originally 140lbs

    original size of liver:
    ML = 0.082 x (140^0.87)
    ML = 6.04

    increased size of liver with 30% increase in MB:
    ML = 0.082 x (182^0.87)
    ML = 7.58

    so..percent increase of liver :

    7.58 - 6.04 = 1.54
    (1.54 / 6.04) x 100 = 25.5% increase

    does that look right?

    -----

    there's this second problem too..basic concept

    Consider an 8-year old child whose body mass is 25 kg and is increasing at a rate of 7 kg/year. Assuming that the mass of the kidneys scales with body mass as Mk=0.021 x Mb^0.85, find the rate at which the mass of the kidneys is increasing (in kg/year).

    For this problem..I basically used the weights 25kg,32kg,39kg, etc..increasing it by 7kg

    the Mk (mass of kidneys) keep increasing my .07. Would that be the answer?
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  2. #2
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    Lexington, MA (USA)
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    Hello, anf9292!

    The mass of a human liver scales allometrically as: . L \:= \:0.082\left(B^{0.87}\right)
    where B is the body mass.

    Suppose the body mass of an individual increases by 30%.
    What is the percent increase in the mass of their liver?

    Here's my work . . . using a person who was originally 140 lbs ...

    It can be dangerous to use a specific number.

    I prefer to solve it in general . . .

    For a body mass of B, the original mass of the liver is: . L_1\:=\:0.082\left(B^{0.87}\right)

    The mass of the larger body is: . B + 0.30B\:=\:1.3B.
    The mass of the liver is: . L_2\:=\:0.082(1.3B)^{0.87} \:=\:0.082\left(1.3^{0.87}\right)\left(B^{0.87}\ri  ght)

    The increase is: . L_2 - L_1\:=\:0.082\left(1.3^{0.87}\right)\left(B^{0.87}  \right) - 0.082\left(B^{0.87}\right)
    . . . . . . . . . . . . . . . . . . =\:0.082\left(B^{0.87}\right)\left(1.3^{0.87} - 1\right)

    The percent increase is: . \frac{L_2-L_1}{L_1} \:=\:\frac{0.82(B^{0.87})(1.3^{0.87}-1)}{0.082(B^{0.87})} \:=\: 1.3^{0.87} - 1


    Therefore, the percent increase is: . 0.256408068 \;\approx\;25.6\%

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