Question

Use the table to answer the question.

Distance Vs. Speed Data
Distance
(ft.) Speed
(ft./sec.)
0 0
1 6.33
2 8.95
3 10.96
4 12.66
The table represents the speed of a free-falling object as a function of distance. Use technology to create a square root function that models this data. Round values to the nearest hundredth.

(1 point)
In the square root function that represents the table of data is s(x)=
x−−√
.

Answer 1

To create a square root function that models the speed (s) as a function of distance (x) based on the provided data, we generally want to assume a form like \( s(x) = k \sqrt{x} \) for some constant \( k \).

To find the value of \( k \), we can use one of the data points from the table. Let's use the point where \( x = 4 \) and \( s(x) = 12.66 \) ft/sec:

\[
s(4) = k \sqrt{4}
\]
\[
12.66 = k \cdot 2
\]
\[
k = \frac{12.66}{2} = 6.33
\]

Now we can plug \( k \) back into the function:

\[
s(x) = 6.33 \sqrt{x}
\]

Now, rounding \( k \) to the nearest hundredth, we have:

\[
s(x) = 6.33 \sqrt{x}
\]

Thus, the square root function that models the data in the table is:

\[
s(x) = 6.33 \sqrt{x}
\]