Question

Question 2
1 pts
This table shows values that represent an exponential function.
X
У
1
1
2
2
4
3
8
4 16
5 32
664
What is the average rate of change for this
function for the interval from x = 3 to x = 5?
1
12
O 12
24
1
24

Answer 1

To calculate the average rate of change of the function from \( x = 3 \) to \( x = 5 \), we will use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( f(a) \) and \( f(b) \) are the function values at points \( a \) and \( b \).

From the table, we have:

- For \( x = 3 \), \( y = f(3) = 8 \)
- For \( x = 5 \), \( y = f(5) = 32 \)

Now, plugging in the values:

\[
\text{Average Rate of Change} = \frac{f(5) - f(3)}{5 - 3}
\]
\[
= \frac{32 - 8}{5 - 3}
\]
\[
= \frac{24}{2} = 12
\]

Thus, the average rate of change for this function from \( x = 3 \) to \( x = 5 \) is **12**.