y = 0.2(1.4)^{x}
what is the approximate average rate of change of the function on the interval 5 ≤ x ≤ 10?
4.71
3.59
2.35
0.94
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Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b=10$, and $f(x)=0.2(1.4)^{x}$.
## Step2: Calculate $f(5)$
$$
\begin{align*}
f(5)&=0.2\times(1.4)^{5}\
&=0.2\times5.37824\
& = 1.075648
\end{align*}
$$
## Step3: Calculate $f(10)$
$$
\begin{align*}
f(10)&=0.2\times(1.4)^{10}\
&=0.2\times28.9254654976\
&=5.78509309952
\end{align*}
$$
## Step4: Calculate the average rate of change
$$
\begin{align*}
\frac{f(10)-f(5)}{10 - 5}&=\frac{5.78509309952- 1.075648}{5}\
&=\frac{4.70944509952}{5}\
&=0.941889019904\approx0.94
\end{align*}
$$

# Answer:
0.94

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \(f(5)\)

Step3: Calculate \(f(10)\)

Step4: Calculate the average rate of change

Answer: