Question

A Non-economic Example of Steady State: There is a well-known relationship between the amount of calories a person consumes and burns, and how much the person weighs. Consider the following relationship:

Suppose calories consumed depends positively on the weight of a person (increases as weight increases) and is given by calories consumed C_c= 14+0.02 W, where W is the weight of the person in kilograms. Calories burned also rises with weight, that is C_b= 2 + 0.18 W. The relation between change in weight, ∆W, C_c and C_b is given by: ∆W=C_c-C_b

a)On a graph where calories consumed and burned is on the y -axis and weight is on the x-axis, plot C_c and C_b

b) Define the steady state as ∆W= 0, that is weight does not change.

Compute the steady state weight and indicate on the graph

c) Suppose a person weighs less than the steady state weight. Will this person be gaining or losing weight? Explain in words using the graph

Answer 1

Answer a :-

Using the above formulas , we can formulate the following table :-

Weight	Calories consumed	Calories burned	W
5	14.1	2.9	11.2
10	14.2	3.8	10.4
15	14.3	4.7	9.6
20	14.4	5.6	8.8
25	14.5	6.5	8
30	14.6	7.4	7.2
35	14.7	8.3	6.4
40	14.8	9.2	5.6
45	14.9	10.1	4.8
50	15	11	4.0
55	15.1	11.9	3.2
60	15.2	12.8	2.4
65	15.3	13.7	1.6
70	15.4	14.6	0.8
75	15.5	15.5	0

Using the above table , we plot the following graph:-

Answer b :-

The steady weight will be 0 when the calories consumed will be equal to calories consumed .

This means that there is no tendency for any change in weight

In the above graph the steady weight is where calories consumed are equal to calories burned that is 75 kgs .

Answer c :-

If the person weights below 75 kgs that is the steady weight then according to the table the calories consumed will be more than the calories burned ,this means he will keep gaining weight until he reaches a point of 75 kgs where he will be at a steady point .