Question

Kevin modeled the height of his son (in inches) at age nn years for n = 2, 3, … , 8 by the sequence

ℎn = 34 + 3.2(n − 2). Interpret the meaning of the constants 34 and 3.2 in his model.

Answer 1

34= height of his son at the age of 2 years.

3.2= rate of increase in height in inches per year.

Explanation:

Kevin made an equation for the height of his son (in inches) as

hₙ=34 + 3.2(n-2) ....... (1) where n is the age of his son in years and its values are 2, 3, 4. ....., 8,...

Now, from this model of the equation, it is clear that at the age of 2 years i.e. n=2, then

h₂=34 inches.

Therefore, 34 inches represents the height of his son at the age of 2 years.

Again when the age is 3 years i.e. n=3, then from equation (1), the height of his son is h₃=34+3.2(3-2) =37.2 inches.

Therefore, it is clear that for each year the height increases by 3.2 inches.

(Answer)