Question

child is 43 inches tall at age 6. For the next few years, the child grows by 2 inches per year. Explain why the child's height after age 6 is a linear function of his age. The child's height after age 6 is a linear function as there is a constant growth rate. Identify the growth rate and initial value. The growth rate is inches/year and the initial value is inches. Using t for time in years since age 6 and H for height in inches, find a formula for H as a linear function of t. H

Answer 1

Answer: H(t) = 43in + (2in/year)*t.

Step-by-step explanation:

At age of 6, the height is 43 inches.

We can define the age of 6 as our t = 0, where t is our variable that represents the number of years after year number 6.

So t = 1 year corresponds to the age of 7 years

t = 2 years corresponds to the age of 8 years, etc.

We know that for the next few years, the child's height will increase by 2 inches per year.

Then at the age of 7, the height will be: 43 in + 2 in

At the age of 8, the height will be: (43in + 2 in) + 2 in = 43in + 2*2in.

And so on, so we can write this as a linear relationship.

H(t) = 43in + (2in/year)*t.

The initial value is the value when t  = 0 years

H(0) = 43in

The initial value is 43 inches.

The growth rate is the coefficient that multiplies the variable, in this case is 2 inches per year or 2 in/year.