A person?s weight depends on both the amount of calories consumed and the energy
used. Moreover, the amount of energy used depends on a person?s weight ? the
average amount of energy used by a person is 17.5 calories per pound per day.
Thus, the more weight a person loses, the less energy the person uses (assuming the
person maintains a constant level of activity). An equation that can be used to
model weight loss is
dW/dt = C/3500 - (17.5/3500)W
where W is the person?s weight (in pounds), t is the time in days, and C is the constant daily
calorie consumption.
(a) Find the function W(t) that gives the person?s weight at day t.
(b) Consider a person who weighs 180 pounds and begins a diet of 2500 calories per day.
How long will it take this person to lose 10 pounds? 35 pounds?
(c) Use a graphing utility to graph the function W(t). What is the limiting weight?
(d) Repeat part (b) and (c) for a person who weighs 200 pounds when the diet is started.
A person?s weight depends on both the amount of calories consumed and the energy
used. Moreover, the amount of energy used depends on a person?s weight ? the
average amount of energy used by a person is 17.5 calories per pound per day.
Thus, the more weight a person loses, the less energy the person uses (assuming the
person maintains a constant level of activity). An equation that can be used to
model weight loss is
dW/dt = C/3500 - (17.5/3500)W
where W is the person?s weight (in pounds), t is the time in days, and C is the constant daily
calorie consumption.
(a) Find the function W(t) that gives the person?s weight at day t.
(b) Consider a person who weighs 180 pounds and begins a diet of 2500 calories per day.
How long will it take this person to lose 10 pounds? 35 pounds?
(c) Use a graphing utility to graph the function W(t). What is the limiting weight?
(d) Repeat part (b) and (c) for a person who weighs 200 pounds when the diet is started.
