find the average rate of change of each function on the given interval.\n1. $f(x)=\\frac{x^{2}+3}{x…

find the average rate of change of each function on the given interval.\n1. $f(x)=\\frac{x^{2}+3}{x - 2};4,9$ 2. $f(x)=\\sqrt{2x - 1};5,25$ \n3. the monthly rainfall in seattle is represented by the function $f(x)=0.16x^{2}-1.99x + 7.56$, where $x$ represents the month and $f(x)$ represents the rainfall. find the average rate of change from july to october.

find the average rate of change of each function on the given interval.\n1. $f(x)=\\frac{x^{2}+3}{x - 2};4,9$ 2. $f(x)=\\sqrt{2x - 1};5,25$ \n3. the monthly rainfall in seattle is represented by the function $f(x)=0.16x^{2}-1.99x + 7.56$, where $x$ represents the month and $f(x)$ represents the rainfall. find the average rate of change from july to october.

Answer

Explanation:

Step1: Determine the values of (x)

July is the 7th month ((x_1 = 7)) and October is the 10th month ((x_2=10)).

Step2: Calculate (f(x_1)) and (f(x_2))

For (x = 7): [ \begin{align*} f(7)&=0.16\times7^{2}-1.99\times7 + 7.56\ &=0.16\times49-13.93 + 7.56\ &=7.84-13.93 + 7.56\ &=1.47 \end{align*} ] For (x = 10): [ \begin{align*} f(10)&=0.16\times10^{2}-1.99\times10 + 7.56\ &=16-19.9+7.56\ &=3.66 \end{align*} ]

Step3: Use the average - rate - of - change formula

The average rate of change formula is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Substitute (x_1 = 7), (x_2 = 10), (f(x_1)=1.47), and (f(x_2)=3.66) into the formula: [ \begin{align*} \frac{f(10)-f(7)}{10 - 7}&=\frac{3.66-1.47}{3}\ &=\frac{2.19}{3}\ &=0.73 \end{align*} ]

Answer:

The average rate of change from July to October is (0.73)