Weight Loss Problem

on3winyoureyes

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a. Harold is going on a diet to lose extra pounds. He currently weighs 200 pounds, and he expects his weight to drop (according to the TV infomercial) at the rate of w'(t)=0.6t-5 pounds per day, where t is the number of days since Harold's diet began. What is the minimum amount of time he should diet if his target weight is 180 pounds? Round to the nearest day.

b. What was Harold's average weight during the diet? Round to the nearest tenth of a pound.





I'm having trouble starting this problem. Is it an exponential decay problem?

180=200^(0.6t-5((k)?

Or is it an optimization problem?
 
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My approach to this problem depends on whether or not you've studied integrals ("antiderivatives"). I'll assume you have, unless you state otherwise. You're given Harold's rate of weight loss as a derivative. What, then, is the function for his actual weight, w(t)? Remember that you also know that w(0) = 200. Now that you have a function for his weight on any given day, what is the smallest integer value of t that will make his weight 180 lbs or less? And for part b, your book should have given you a nice formula to calculate the average value of a function over a closed interval. What do you get if you apply that formula?
 
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