Question

Jennifer is taking a speed reading course. She records m(t), the most number of words that she can read in a minute (wpm), after t weeks of beginning the course.

t 1 2 3 4 5 6
m(t) 124 160 220 304 412 544

According to the table, what is the average rate of change over the interval [1, 4]?
A.
180 wpm per week
B.
60 wpm per week
C.
144 wpm per week
D.
48 wpm per week

Answer 1

To find the average rate of change of \( m(t) \) over the interval \([1, 4]\), we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{m(t_2) - m(t_1)}{t_2 - t_1}
\]

In this case, we have \( t_1 = 1 \) and \( t_2 = 4 \).

From the table, we can find:

- \( m(1) = 124 \) wpm
- \( m(4) = 304 \) wpm

Now we can substitute these values into the formula:

\[
\text{Average Rate of Change} = \frac{m(4) - m(1)}{4 - 1} = \frac{304 - 124}{4 - 1} = \frac{180}{3} = 60 \text{ wpm per week}
\]

Thus, the average rate of change over the interval \([1, 4]\) is:

**B. 60 wpm per week**