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

315−231/5−1≈21
the fraction with numerator 315 minus 231 and denominator 5 minus 1 almost equal to 21

252−231/2−1≈21
the fraction with numerator 252 minus 231 and denominator 2 minus 1 almost equal to 21

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

252−2/231−1≈1.1

Answer 1

To calculate the rate of change of the weight of the baby elephant from interval 1 to 2 (which corresponds to t = 1 week and t = 2 weeks), we use the formula for the average rate of change, which is:

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

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

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

Plugging these values into the formula:

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

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

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