Question

the function (g(x)=3.9sqrt{x}+0.2) models the median height, (g(x)), in inches, of children who are (x) months of age. the graph of (g) is shown.

according to the model, what is the median height of children who are 24 months, or 2 years, old? use a calculator to find the median height.
the median height is (square) inches. (round to the nearest tenth of an inch.)

a. stretch (f(x)) vertically by a factor of 3.9. shift (f(x)) up by 0.2 units.
b. shrink (f(x)) vertically by a factor of 3.9. shift (f(x)) up by 0.2 units.
c. stretch (f(x)) vertically by a factor of 3.9. shift (f(x)) right by 0.2 units.

Explanation:

Step1: Substitute x - value

We are given the function $g(x)=3.9\sqrt{x}+ 0.2$ and we need to find the median height when $x = 24$ (months). Substitute $x = 24$ into the function: $g(24)=3.9\sqrt{24}+0.2$.

Step2: Calculate square - root

First, find $\sqrt{24}\approx4.899$. Then multiply by 3.9: $3.9\times4.899 = 19.1061$.

Step3: Add 0.2

Now add 0.2 to the result: $19.1061+0.2=19.3061$.

Step4: Round to nearest tenth

Rounding 19.3061 to the nearest tenth gives 19.3.

Answer:

19.3 inches