Use the table to answer the question. Capacity of Rain Barrel (L) Radius of Rain Barrel (cm) 150 23.16 200 26.75 250 29.90 300 32.76 350 35.38 A factory produces many different rain barrels. All the rain barrels are the same height, but their radii vary. The table shows the radius of a rain barrel as a function of its capacity. Use technology to create a square root function that fits the table of data. (1 point) Responses The radius of a rain barrel as a function of its capacity is modeled by the function r(x)=x−−√+14.09 . The radius of a rain barrel as a function of its capacity is modeled by the function r left parenthesis x right parenthesis equals square root of x plus 14.09 . The radius of a rain barrel as a function of its capacity is modeled by the function r(x)=1.89x−−√ . The radius of a rain barrel as a function of its capacity is modeled by the function r left parenthesis x right parenthesis equals 1.89 square root of x . The radius of a rain barrel as a function of its capacity is modeled by the function r(x)=0.53x−−√ . The radius of a rain barrel as a function of its capacity is modeled by the function r left parenthesis x right parenthesis equals 0.53 square root of x . The radius of a rain barrel as a function of its capacity is modeled by the function r(x)=x−−√+10.91 .

Answer 1

To create a square root function that models the radius of a rain barrel as a function of its capacity, we can analyze the data given in the table. The table shows the following values:

| Capacity (L) | Radius (cm) | |--------------|-------------| | 150 | 23.16 | | 200 | 26.75 | | 250 | 29.90 | | 300 | 32.76 | | 350 | 35.38 |

We can try to find a function of the form:

\[ r(x) = a\sqrt{x} + b \]

where \( r(x) \) is the radius and \( x \) is the capacity.

Using technology (like a graphing calculator or statistical software), you can perform a regression analysis to find the constants \( a \) and \( b \). After fitting a square root function to the data, you will likely arrive at one of the following equations presented in the choices.

Confirm that the model fits the data well.

Upon reviewing the options provided, you will check which equation aligns well with the estimates from your regression analysis.

Given the items listed, the correct answer appears to involve a function of the form:

• The radius of a rain barrel as a function of its capacity is modeled by the function \( r(x) = 0.53\sqrt{x} + 10.91 \).

You would want to verify that this equation correctly outputs the radius values for the respective capacity inputs from the table.

Please check to ensure that this is indeed the best-fitting equation by substituting the values from the table into the equation and checking their correctness!