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h = 3a + 28.6A pediatrician uses the model above to estimate the height h of a b...


Question

h = 3a + 28.6

A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?

Options

A)
3
B)
5.7
C)
9.5
D)
14.3

The correct answer is A.

Explanation:

Choice A is correct. In the equation h D + 28.6, if D, the age of the boy, increases by 1, then h becomes h = 3(a+1) + 28.6 = 3a + 3 + 28.6 = (3a + 28.6) + 3. Therefore, the model estimates that the boy's height increases by 3 inches each year.
Alternatively: The height, h, is a linear function of the age, a, of the boy. The coefficient 3 can be interpreted as the rate of change of the function; in this case, the rate of change can be described as a change of 3 inches in height for every additional year in age.
Choices B, C, and D are incorrect and are likely the result of dividing 28.6 by 5, 3, and 2, respectively. The number 28.6 is the estimated height, in inches, of a newborn boy. However, dividing 28.6 by 5, 3, or 2 has no meaning in the context of this question.


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