Question

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

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

315−2315−1≈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

252+2312+1≈241.5

Answer 1

To calculate the rate of change for the interval from week 1 to week 2 (i.e., from \(t = 1\) to \(t = 2\)), we use the formula for the average rate of change, which is given by:

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

In this case:

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

Substituting these values into the formula:

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

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

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

Thus, the correct response is:

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