1. ## 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?

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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?

2. Hello, anf9292!

The mass of a human liver scales allometrically as: .$\displaystyle L \:= \:0.082\left(B^{0.87}\right)$
where $\displaystyle B$ 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 $\displaystyle B$, the original mass of the liver is: .$\displaystyle L_1\:=\:0.082\left(B^{0.87}\right)$

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

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

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

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