Question

Use the table to answer the question. t 0 1 2 3 4 h(t) 3 5 7 4 2 The table denotes the height reached by a basketball, in feet, t seconds after being thrown. Calculate the rate of change in the basketball’s height between the first and fourth second.(1 point)

Answer 1

To calculate the rate of change in the basketball's height between the first and fourth seconds, we can use the formula for the average rate of change, which is given by:

\[
\text{Average rate of change} = \frac{h(t_2) - h(t_1)}{t_2 - t_1}
\]

In this case, \(t_1 = 1\) second and \(t_2 = 4\) seconds. From the table, we have:

- \(h(1) = 5\) feet
- \(h(4) = 2\) feet

Now we can plug these values into the formula:

\[
\text{Average rate of change} = \frac{h(4) - h(1)}{4 - 1} = \frac{2 - 5}{4 - 1} = \frac{-3}{3} = -1
\]

Therefore, the rate of change in the basketball's height between the first and fourth second is \(-1\) feet per second.