Calculating Kidney Mass Increase in an 8-Year Old Child

[anf9292]

Homework Statement

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).

Homework Equations

Mk=0.021 x Mb^0.85

The Attempt at a Solution

Mk=0.021 x 25^0.85
Mk=0.021 x 32^0.85
Mk=0.021 x 39^0.85

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?

 

[anathema]

Thank you for your question. Based on the given information, we can calculate the rate at which the mass of the kidneys is increasing by using the formula Mk=0.021 x Mb^0.85, where Mb is the body mass and Mk is the mass of the kidneys.

Using the given values, we can calculate the mass of the kidneys for the 8-year-old child as follows:

Mk=0.021 x 25^0.85
Mk= 0.021 x 16.6
Mk= 0.3486 kg

This means that the mass of the kidneys for the 8-year-old child is approximately 0.3486 kg. Now, to calculate the rate at which the mass of the kidneys is increasing, we can use the following formula:

rate of increase = (Mk2 - Mk1)/(t2 - t1)

Where Mk2 is the mass of the kidneys after a certain period of time, Mk1 is the initial mass of the kidneys, t2 is the final time, and t1 is the initial time.

In this case, we can use the information that the body mass is increasing at a rate of 7 kg/year. This means that after one year, the body mass will be 25 kg + 7 kg = 32 kg. Therefore, after one year, the mass of the kidneys will be:

Mk=0.021 x 32^0.85
Mk=0.021 x 22.8
Mk=0.4788 kg

Now, we can plug in the values in the formula for the rate of increase:

rate of increase = (0.4788 kg - 0.3486 kg)/(1 year)
rate of increase = 0.1302 kg/year

Therefore, the rate at which the mass of the kidneys is increasing is 0.1302 kg/year. This means that for every year, the mass of the kidneys will increase by approximately 0.1302 kg.

I hope this helps to answer your question. Let me know if you have any further questions. Thank you!
Scientist

 

[m2003]

I would like to first acknowledge the use of appropriate equations and the attempt to solve the problem. However, I would like to provide a more thorough solution and explanation.

To calculate the rate at which the mass of the kidneys is increasing, we first need to understand the relationship between body mass and kidney mass. The given equation, Mk=0.021 x Mb^0.85, suggests that the mass of the kidneys is proportional to the 0.85 power of the body mass. This means that as the body mass increases, the mass of the kidneys will also increase but at a slower rate.

To find the rate at which the mass of the kidneys is increasing, we need to take the derivative of the equation with respect to time (t).

dMk/dt = 0.021 x 0.85 x Mb^(-0.15) x dMb/dt

Substituting the given values, we get:

dMk/dt = 0.021 x 0.85 x (25)^(-0.15) x 7

dMk/dt = 0.0153 kg/year

This means that the mass of the kidneys is increasing at a rate of 0.0153 kg per year in the 8-year old child. It is important to note that this is a general estimate and may vary based on individual factors such as diet, exercise, and overall health.

In conclusion, the correct way to calculate the rate at which the mass of the kidneys is increasing in an 8-year old child is by taking the derivative of the given equation with respect to time. This will provide a more accurate and precise answer.