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+2312+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
the fraction with numerator 315 minus 231 and denominator 5 minus 1 almost equal to 21

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

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

Answer 1

To calculate the rate of change of the baby elephant's weight from week 1 to week 2, we can use the following formula:

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

In this interval:

- \(w(t_1) = w(1) = 231\) lbs (weight at week 1)
- \(w(t_2) = w(2) = 252\) lbs (weight at week 2)
- \(t_1 = 1\)
- \(t_2 = 2\)

Plugging these values into the formula gives:

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

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

\[
\frac{252 - 231}{2 - 1} ≈ 21
\]

So the correct answer is:

**252−2312−1≈21**