Growth in height: Between the ages of 7 and 11 years, a certain boy grows 2 inches taller each year. At age 9 he is 48 inches tall. a. Explain why, during this period, the function giving the height...

Growth in height: Between the ages of 7 and 11 years, a certain boy grows 2 inches taller each year. At age 9 he is 48 inches tall.

a. Explain why, during this period, the function giving the height of the boy in terms of his age is linear. Identify the slope of this function.

b. Use a formula to express the height of the boy as a linear function of his age during this period. Be sure to identify what the letters that you use mean.

c. What is the initial value of the function you found in part b?

d. Studying a graph of the boy’s height as a function of his age from birth to age 7 reveals that the graph is increasing and concave down. Does this indicate that his actual height (or length) at birth was larger or smaller than your answer to part c? Be sure to explain your reasoning.