A 200 pound man starts a weight loss regimen that promises a loss of 1 percent of body weight per week.
How many weeks will it take to reach his goal of 150 pounds?
The weight loss program has diminishing effectiveness each week.
In the first week, he will lose 200(0.01) = 2 pounds so he will weigh in at 198 pounds. In the second, he will lose a bit less weight: only 198(0.01) = 1.98 pounds. Each successive week he will weigh in lighter and therefore lose a bit less weight.
The easiest way to solve this problem is to track his weekly weight. If he loses 1 percent per week; that means each week he will weigh in at 99 percent of his previous week’s weight.
In other words:
Wt = 0.99Wt-1
We know that his initial weight is 200, so the formula for weight after n weeks is:
Wn = 0.99Wn-1 = (0.99)2 Wn-2 = … = 200(0.99)n
We solve this equation for the target of 150 pounds to find:
150 = 200(0.99)n => n = (log150/200)/log0.99 = 28.62…
Therefore, he will drop below 150 pounds at the 29th week. Of course few people have the discipline to stay on a diet for over half a year, and that’s perhaps one of the reasons weight loss is hard.