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

Question

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

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

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

315−2315−1≈21
the fraction with numerator 315 minus 231 and denominator 5 minus 1 almost equal to 21

Answer 1

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

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

Here, \(t_1 = 1\) and \(t_2 = 2\), so we have:

• \(w(1) = 231\)
• \(w(2) = 252\)

Now substitute the values:

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

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

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

The corresponding response is:

252−2312−1≈21

This indicates the change in weight from 231 lbs to 252 lbs over the change in time from 1 week to 2 weeks, which gives an average rate of change of approximately 21 lbs per week.