Question

a table of values, rounded to the nearest hundredth, for the function ( y = sqrt3{x} ) is given for ( 0 leq x leq 8 ). what is the average rate of change of the function over the interval 2, 7 to the nearest hundredth?

( x )	( y )
1	1.00
2	1.26
3	1.44
4	1.59
5	1.71
6	1.82
7	1.01
8	2.00

options: 0.05, 0.35, 1.62, 0.13

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( y = f(x) \) over the interval \([a, b]\) is given by \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify the values of \(a\), \(b\), \(f(a)\), and \(f(b)\)

For the interval \([2, 7]\), we have \(a = 2\), \(b = 7\). From the table, when \(x = 2\), \(y = f(2)=1.26\) and when \(x = 7\), \(y = f(7)=1.91\) (assuming the typo in the table is corrected, it should be \(1.91\) instead of \(1.01\) as \(\sqrt[3]{7}\approx1.91\)).

Step3: Substitute the values into the formula

\[
\text{Average rate of change}=\frac{f(7)-f(2)}{7 - 2}=\frac{1.91 - 1.26}{5}=\frac{0.65}{5}=0.13
\]

Answer:

\(0.13\)