Question

Determine the difference between the rate of change g(x) over the interval [9,49] and the rate of change of g(x) over the interval [25,81]. Round Your answer to the nearest hundredth.(b) Which is the following values represent the rate of change over the interval [121,225]1/13 1/11 2/13 2/11

Answer 1

Part A

g(9) = 6

g(49) = 14

The rate of change g(x) over the interval [9,49] is:

$\frac{g(49)-g(9)}{49-9}=\frac{14-6}{40}=\frac{8}{40}=\frac{1}{5}$

Likewise:

g(25)=10

g(81)=18

The rate of change of g(x) over the interval [25,81] is:

$\frac{g(81)-g(25)_{}}{81-25}=\frac{18-10}{56}=\frac{8}{56}=\frac{1}{7}$

The difference will be:

$\begin{gathered} =\frac{1}{5}-\frac{1}{7} \\ =0.06\text{ (to the nearest hundredth)} \end{gathered}$

Part B

g(121)=11 x 2=22

g(225)= 15 x 2 =30

Therefore, the rate of change over the interval [121,225]

$=\frac{g(225)-g(121)}{225-121}=\frac{30-22}{104}=\frac{8}{104}=\frac{1}{13}$