The table below gives, for a certain man, his height H = H(t) in inches at age t in years. t = Age (years) H = Height (inches) 0 22.5 5 42.0 10 15 20 25 56.5 66.0 73.0 73.5 (a) Use functional notation to express the height of the man at age 11, and then estimate its value. (Round the height to one decimal place.) H( inches (b) Now we study the man's growth rate. (i) Make a table showing, for each of the 5-year periods, the average yearly growth rate-that is, the average yearly rate of change in H. (Round the answers to one decimal place.) Age range 0 to 5 Average yearly growth rate (ii) During which 5-year period did the man grow the most in height? 0 to 5 5 to 10 10 to 15 15 to 20 20 to 25 5 to 10 (iii) Describe the general trend in the man's growth rate. There is no trend as the man gets older. As the man gets older, his growth is constant. As the man gets older, he grows more slowly. As the man gets older, he grows more quickly. (c) What limiting value would you estimate for the height of this man? inches Explain your reasoning in physical terms. 10 to 15 15 to 20 20 to 25