my attempt at this word problem?

Question

1. Problem with variables

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). Hint: some differential calculus will help guide you to the answer.

2. Relevant equations
Mk = 0.021 x Mb^0.85

3. Attempt at problem

I basically chose the weights 25, 32, 39 etc..each 7 kg apart

Mk = 0.021 x 25^0.85
Mk = 0.021 x 32^0.85
Mk = 0.021 x 32^0.85

The mass of the kidney increased my .07 every time..so would that be the rate of increase?

Answer 1

You got the correct answer. Here is how you find it using differential calculus.

From the given eq. we have
dM(K)/dt = .021 x .85 M(b)^-.15 dM(b)/dt

plug in the initial conditions M(b) = 25 and dM(b)/dt = 7 and you will find that dM(k)/dt = .077 kg yr^-1