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A study of American girls ages 4-13 in the 90th percentile found that their height h (in cm) as a function of their age a (in years) satisfies the equation h(a) = 6.42a +82.2. The same study found that their weight W (in g) as a function of their height is given by W(h) = 0.0304h².85. 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. W(a) = Differentiate this function to find W'(a) using the chain rule. dW da c. What is the rate of change in weight at ages 3, 7, and 13? W'(3) = g/yr

A study of American girls ages 4-13 in the 90th percentile found that their height h (in cm) as a function of their age a (in years) satisfies the equation h(a) = 6.42a +82.2. The same study found that their weight W (in g) as a function of their height is given by W(h) = 0.0304h².85. 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. W(a) = Differentiate this function to find W'(a) using the chain rule. dW da c. What is the rate of change in weight at ages 3, 7, and 13? W'(3) = g/yr

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 1TI: Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use...
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A study of American girls ages 4-13 in the 90th percentile found that their height h (in cm) as a function of their age a (in years) satisfies the equation h(a) = 6.42a + 82.2. The same study found that their weight W (in g) as a function of their height is given by W(h) = 0.0304h2.85 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. W(a) = Differentiate this function to find W'(a) using the chain rule. dW da c. What is the rate of change in weight at ages 3, 7, and 13? W'(3)= g/yr W'(7) = g/yr W'(13) = = g/yr
Transcribed Image Text:A study of American girls ages 4-13 in the 90th percentile found that their height h (in cm) as a function of their age a (in years) satisfies the equation h(a) = 6.42a + 82.2. The same study found that their weight W (in g) as a function of their height is given by W(h) = 0.0304h2.85 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. W(a) = Differentiate this function to find W'(a) using the chain rule. dW da c. What is the rate of change in weight at ages 3, 7, and 13? W'(3)= g/yr W'(7) = g/yr W'(13) = = g/yr
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