Question

The weight, w, of a baby elephant is shown in the table, where t is the number of weeks of growth.

t (in weeks) 0 1 2 3 4 5
w (in lbs) 210 231 252 273 294 315
Which equation shows how to calculate the rate of change for interval 1 to 2?

(1 point)
Responses

252−2/231−1≈1.1

252+231/2+1≈241.5

252−231/2−1≈21

315−231/5−1≈21

Answer 1

To calculate the rate of change for the interval from \(t = 1\) to \(t = 2\), we will use the formula for the rate of change, which is:

\[
\text{Rate of change} = \frac{w(t_2) - w(t_1)}{t_2 - t_1}
\]

In this case, \(t_1 = 1\) and \(t_2 = 2\).

From the table, we have:
- \(w(1) = 231\) lbs
- \(w(2) = 252\) lbs

Now, substituting these values into the formula gives us:

\[
\text{Rate of change} = \frac{252 - 231}{2 - 1} = \frac{21}{1} = 21
\]

Thus, the equation that shows how to calculate the rate of change for the interval from 1 to 2 is:

\[
\frac{252 - 231}{2 - 1} \approx 21
\]

So the correct response is:

**252−231/2−1≈21**