Question

15
Fill in the Blank 1 point
This table shows values represented by an exponential function.
1
1
3
2
9
3 27
4 64
5 125
6216
The average rate of change for this function for the interval from x= 3 to x = 5 isl
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98
76
37
49

Answer 1

To find the average rate of change of the exponential function for the interval from \( x = 3 \) to \( x = 5 \), you can use the formula:

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

where:
- \( f(a) \) is the function value at \( x = a \),
- \( f(b) \) is the function value at \( x = b \),
- \( a \) is the starting point (3 in this case), and
- \( b \) is the endpoint (5 in this case).

From the values provided in the table, we can find:
- \( f(3) = 27 \)
- \( f(5) = 125 \)

Now we can plug these values into the formula with \( a = 3 \) and \( b = 5 \):

\[
\text{Average Rate of Change} = \frac{f(5) - f(3)}{5 - 3} = \frac{125 - 27}{5 - 3} = \frac{98}{2} = 49
\]

Thus, the average rate of change for this function from \( x = 3 \) to \( x = 5 \) is **49**.