What would be the expected difference in height between a child 25 months of age and a child 16 months of​ age?

Question

The average height of a boy in the United​ States, from birth through 60​ months, can be modeled by

y=2.9√x+20.1 where y is the average​ height, in​ inches, of boys who are x months of age. What would be the expected difference in height between a child 25 months of age and a child 16 months of​ age?

Answer 1

For a child 25 months of age, the height would be y = 2.9√25 + 20.1 or 2.9(5) + 20.1

For a child 16 months of age, the height would be y = 2.9√16 + 20.1 or 2.9(4) + 20.1

Therefore, the difference would be 2.9(5) + 20.1 - [2.9(4) + 20.1].

By rearranging this, we can arrive at 2.9(5) - 2.9(4) + 20.1 - 20.1.

By factoring out 2.9 from the first 2 terms, we can simplify to 2.9(5-4) + 0 = 2.9(1) = 2.9 inches.

The difference in heights between these 2 kids would be 2.9 inches.