Chapter 7, Problem 24RE

To determine

To formulate : the differential equation and solve it to find her weight as a function

Answer to Problem 24RE

The equilibrium weight of Barbara is $50kg$

Explanation of Solution

Given information : The question is

Barbara weight $60kg$ and it’s on diet of $1600$ calories per day of which $850$ are used automatically by basal metabolism. She spend $15/cal/kg/day$ times weight by doing exercise. If $1kg$ of fat contains $10,000$ calories then assume the storage of calories in the form of fat is $100\%$ efficient

Calculation :

Calorie input/day $=1600$

Calorie burned/day $=850+15w$

Net calories/day $=1600-\left(850+15w\right)=750-15w$

Weight change per day $=\frac{dw}{dt}=\frac{750-15w}{10000}$

So, $\frac{dw}{dt}=0$ when $750-15w=0$ that gives $w=50$

Therefore, equilibrium weight of Barbara is $50kg$