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?

Answer 1

To calculate the rate of change of the weight \( w \) of the baby elephant from week \( t = 1 \) to week \( t = 2 \), we use the formula for the rate of change:

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

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

From the given data:
- Weight at \( t = 1 \): \( w(1) = 231 \) lbs
- Weight at \( t = 2 \): \( w(2) = 252 \) lbs

Now we substitute these values into the formula:

\[
\text{Rate of Change} = \frac{w(2) - w(1)}{2 - 1} = \frac{252 - 231}{2 - 1} = \frac{21}{1} = 21 \, \text{lbs/week}
\]

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

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

This indicates that the weight of the baby elephant increases by 21 pounds per week between week 1 and week 2.