Answer:
[tex]x(35)\approx 11.8[/tex]
Step-by-step explanation:
Modeling With Functions
We have a table of values of speeds vs distance taken for a car to stop. We are required to find a model that uses the square root and fits the given data to predict other values of d as a function of v.
By the nature of the problem, we can know that for v=0, d must be 0 too. So our model won't include a vertical shift or independent term. Being v the speed of the car and x the distance it takes to stop, we use the following model
[tex]x(v)=A\sqrt{v}[/tex]
We must find A to make the function fit the data. Let's use the first point (v,x); (20,9)
[tex]9=A\sqrt{20}[/tex]
Solving for A
[tex]\displaystyle A=\frac{9}{\sqrt{20}}[/tex]
[tex]A\approx 2[/tex]
Then we have
[tex]x(v)=2\sqrt{v}[/tex]
Evaluating for v=35
[tex]x(35)=2\sqrt{35}=11.83[/tex]
[tex]\boxed{x(35)\approx 11.8}[/tex]
Last option
