Question

Hours (x)|Money (y)
0|0
2.5|48.45
6|116.28
8.75|169.58
10.25|198.65
What is the rate of change for the interval 2.5-8.75? Round your answer to the nearest cent
10.25|

Answer 1

To find the rate of change for the interval from \( x = 2.5 \) to \( x = 8.75 \), we can use the formula for the average rate of change, which is given by:

\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

In this case:
- \( x_1 = 2.5 \), \( y_1 = 48.45 \)
- \( x_2 = 8.75 \), \( y_2 = 169.58 \)

Now, we can substitute these values into the formula:

\[
\text{Rate of Change} = \frac{169.58 - 48.45}{8.75 - 2.5}
\]

Calculating the numerator:

\[
169.58 - 48.45 = 121.13
\]

Calculating the denominator:

\[
8.75 - 2.5 = 6.25
\]

Now substituting back into the formula:

\[
\text{Rate of Change} = \frac{121.13}{6.25}
\]

Calculating the rate:

\[
\text{Rate of Change} = 19.3816
\]

Rounding to the nearest cent, we get:

\[
\text{Rate of Change} \approx 19.38
\]

So the rate of change for the interval from \( 2.5 \) to \( 8.75 \) is approximately **19.38**.