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Chapter 8: Problem 67

My weight increased by \(1 \%\) in January and \(1 \%\) in February, so my increase in weight over the two months is \(2 \%\).

Short Answer

Expert verified
The actual increase in weight over the two months, considering the gains are compounded, is approximately 2.01%

Step by step solution

01

Express January's weight gain

Express the weight gain in January as a multiplication factor. If weight gained is 1%, new weight after January will be 1.01 times the original weight, assuming original weight as 1 unit.
02

Express February's weight gain

Similar to Step 1, weight gain in February over the weight after January is again a multiplication factor of 1.01. Consequently, the total weight after February is \(1.01 \times 1.01\) times original weight.
03

Calculate total weight gain

Now calculate the new weight after two months. It will be slightly more than the original weight. Subtract 1 (original weight) from total weight to get the percentage increase of weight. The answer is multiplied by 100 to get the percentage.
04

Convert result to percentage

Convert the result to a percentage by multiplying by 100.

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