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

252−2231−1≈1.1
252
−
2
231
−
1
≈
1.1
the fraction with numerator 252 minus 2 and denominator 231 minus 1 almost equal to 1 point 1
252−2312−1≈21
252
−
231
2
−
1
≈
21
the fraction with numerator 252 minus 231 and denominator 2 minus 1 almost equal to 21

252+2312+1≈241.5
252
+
231
2
+
1
≈
241.5
the fraction with numerator 252 plus 231 and denominator 2 plus 1 almost equal to 241 point 5

315−2315−1≈21

Answer 1

To calculate the rate of change of the weight of the baby elephant from week 1 to week 2, we can use the formula for the average 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 \( t_2 = 2 \). The respective weights \( w(1) \) and \( w(2) \) are:

- \( w(1) = 231 \) lbs
- \( w(2) = 252 \) lbs

Now substituting these values into the formula:

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

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

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

So the correct response is:

**252−2312−1≈21** (the fraction with numerator 252 minus 231 and denominator 2 minus 1 almost equal to 21).