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:

`(g(49)-g(9))/(49-9)=(14-6)/(40)=(8)/(40)=(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}=(18-10)/(56)=(8)/(56)=(1)/(7)`

The difference will be:

`\begin{gathered} =(1)/(5)-(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]

`=(g(225)-g(121))/(225-121)=(30-22)/(104)=(8)/(104)=(1)/(13)`