In Example 8, change “weight and height both increase by 5%” to “weight increases by 10% and height increases by 5%” and then solve the resulting problem.

Data from Example 8

A person’s body mass index (BMI) is directly proportional to their weight and inversely proportional to the square of their height. If weight and height both increase by 5%, by what factor does the BMI change?

The original BMI is given by

where w₀ and h₀ represent the original weight and height, respectively. After the weight and height increase by 5%, their new values will be 1.05w₀ and 1.05h₀.Thus, the new BMI is

Therefore, the BMI changes by a factor of 0.952. This means the new BMI is 95.2% of the original BMI.

BMI original kwo ho 2