find the average rate of change of each function on the given interval.
1. $f(x)=\frac{x^{2}+3}{x - 2};4,9$ 2. $f(x)=\sqrt{2x - 1};5,25$
3. 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.

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Accepted 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 $0.73$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the values of \(x\)

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

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

Answer: