Question

A study of American girls ages 4-13 in the 90?ℎ percentile found that their height ℎ (in cm) as a function of their age ? (in years) satisfies the equation

ℎ(?)=6.42?+81.9

The same study found that their weight ? (in g) as a function of their height is given by

?(ℎ)=0.0305ℎ2.84.

a. What is a rate of growth in height? Rate of Growth = cm/yr

b. Write an expression for the composite function that gives the weight as a function of age. ?(?)=

Differentiate this function to find ?′(?) using the chain rule. ????=

c. What is the rate of change in weight at ages 3, 11, and 14?

?′(3)= g/yr

?′(11)= g/yr

?′(14)= g/yr

Answer 1