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?

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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:

*W*_{t}**= 0.99**

*W*_{t}_{-1}
We
know that his initial weight is 200, so the formula for weight after

*n*weeks is:

*W*_{n}**= 0.99**

*W*_{n}_{-1}= (0.99)^{2}*W*_{n}_{-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.

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