According to a simple physiological model, an athletic adult male 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. Suppose that a particular person has a constant caloric intake of H calories per day. Let W(t) be the person's weight in pounds at time t (measured in days). (a) What differential equation has solution W(t)? dW dt (Your answer may involve W, H and values given in the problem.) (b) Solve this differential equation, if the person starts out weighing 165 pounds and consumes 3500 calories a day. W = (c) What happens to the person's weight as t→ ∞o? W →
According to a simple physiological model, an athletic adult male 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. Suppose that a particular person has a constant caloric intake of H calories per day. Let W(t) be the person's weight in pounds at time t (measured in days). (a) What differential equation has solution W(t)? dW dt (Your answer may involve W, H and values given in the problem.) (b) Solve this differential equation, if the person starts out weighing 165 pounds and consumes 3500 calories a day. W = (c) What happens to the person's weight as t→ ∞o? W →
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:According to a simple physiological model, an athletic adult male 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.
Suppose that a particular person has a constant caloric intake of H calories per day. Let W(t) be the person's weight in pounds at time t (measured in
days).
(a) What differential equation has solution W(t)?
-0
(Your answer may involve W, H and values given in the problem.)
dW
dt
(b) Solve this differential equation, if the person starts out weighing 165 pounds and consumes 3500 calories a day.
W =
(c) What happens to the person's weight as t → ∞o?
W
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