SATMathematics Practice Test 1

Question : 6 of 58

Marks: +1, -0

$h=3a+28.6$
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?

3
5.7
9.5
14.3

Validate

Solution:

In the equation

h=3a+28.6

,if a, 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 to result from common errors in calculating the value of h or in calculating the difference between the values of h for different values of a.

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