Question

quickish question about modeling differential equations

Answer 1

According to a simple physiological model, an athletic adult needs 20 calories per day per pound of body weight to maintain his weight.
If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference
between the number of calories consumed and the number needed to maintain his current weight. The constant of proportionality
is 1/3500 pounds per calorie.

Answer 2

so \[\frac{dW}{dt}=some..constant(difference..in..calories)\]
Suppose a person has a constant caloric intake of 2700 calories per day. Write a differential equation for W(t). Use upper case W.

Answer 3

i'm stuck on how to think about this

Answer 4

If the person's weight is W, in pounds,
Then to maintain body weight W, he must consume 20W calories per day.

If he does not, then the rate of change of his weight, W',
will be,\[\large\rm W'=C-20W\]Where C is amount of calories the person is taking in daily.

I'm not sure how the constant of proportionality fits into this.. hmm
Do they mean like this?\[\large\rm W'=k(C-20W)\]Hmmm I dunno :[

Answer 5

yes? I honestly don't know.
C=2700

Answer 6

doesn't work.

Answer 7

W(t) = person's weight in lbs at time t

(20 calories/1 pound)*(W(t) pounds) = 20*W(t) calories

to maintain the weight, the person must consume 20*W(t) calories
it says that the person actually takes in 2700 calories per day


difference = (actual intake) - (needed intake)
difference = (2700) - (20W)
difference = 2700 - 20W


so I'm thinking it should be

dW/dt = k*(2700 - 20W)

Answer 8

`The constant of proportionality is 1/3500 pounds per calorie`
so it looks like k = 1/3500

Answer 9

ok that make sense