Question

Given that $ h = 3a + 28.6 $
A paediatrician 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?
A.3
B.5.7
C.9.5
D.14.3

Answer 1

Hint: To find the increment in the height of the boy each year we will use the given expression. We will substitute the age in the expression of height to get the respective height. Then to find the final answer, we will find the difference between the ages of two consecutive years.

Complete step-by-step answer:
Step by step answer:
The expression for the height of boy is given as $ h = 3a + 28.6 $ .
Where, $ h $ is height in inches and $ a $ is the age of the boy.
We can write the above expression for the age of 2 years.
\[\begin{array}{l}
h = \left( {3 \times 2 + 28.6} \right)\,\,{\rm{inches}}\\
h = \left( {6 + 28.6} \right)\,{\rm{inches}}\\
h = 32.6\;{\rm{inches}}
\end{array}\]
Now we will find the height for the year next to 2, since we need to find the increment each year. Hence, we will find the height for the age of 3 years.
We can write the expression for the age of 3 years, we get,
\[\begin{array}{l}
h = \left( {3 \times 3 + 28.6} \right)\,\,{\rm{inches}}\\
h = \left( {9 + 28.6} \right)\,{\rm{inches}}\\
h = 35.6\;{\rm{inches}}
\end{array}\]
To find the increment in the height each year, we can subtract the above expression.
\[\begin{array}{c}
{\rm{Estimated Increase}} = \left( {35.6 - 32.6} \right)\;{\rm{inches}}\\
 = 3\;{\rm{inches}}
\end{array}\]
Hence the estimated increase in height each year is $ {\rm{3}}\;{\rm{inches}} $ and option (A) is correct.
So, the correct answer is “Option A”.

Note: In the question range of age is given between 2 and 5 years, but we need to find the increment each year. For this we will calculate the height from the given expression for the age of 2 and 3 not 5. We can do calculation on the basis of any two consecutive years between 2 and 5.