Question

The weight, in pounds, of a newborn baby tt months after birth can be modeled by W, .W. The table below has select values showing the linear relationship between tt and W, .W. Determine the number of pounds the baby gains per month.
tt WW
55 12, point, 2, 512.25
77 14, point, 7, 514.75
99 17, point, 2, 517.25

Answer 1

To determine the number of pounds the baby gains per month based on the provided table, we can calculate the weight gain per month using the values of \( W \) (weight) and \( t \) (months after birth).

Here are the data points you provided:

\[
\begin{array}{|c|c|}
\hline
t & W \\
\hline
5 & 12.25 \\
7 & 14.75 \\
9 & 17.25 \\
\hline
\end{array}
\]

We will calculate the weight gain for the intervals between the given months.

**1. From \( t = 5 \) to \( t = 7 \):**

Weight at \( t = 5 \) is \( 12.25 \) lbs.
Weight at \( t = 7 \) is \( 14.75 \) lbs.
Weight gain over this interval:
\[
\text{Weight gain} = W(7) - W(5) = 14.75 - 12.25 = 2.50 \text{ lbs}
\]
Time interval:
\[
\Delta t = 7 - 5 = 2 \text{ months}
\]
Weight gain per month:
\[
\text{Gain per month} = \frac{2.50 \text{ lbs}}{2 \text{ months}} = 1.25 \text{ lbs/month}
\]

**2. From \( t = 7 \) to \( t = 9 \):**

Weight at \( t = 7 \) is \( 14.75 \) lbs.
Weight at \( t = 9 \) is \( 17.25 \) lbs.
Weight gain over this interval:
\[
\text{Weight gain} = W(9) - W(7) = 17.25 - 14.75 = 2.50 \text{ lbs}
\]
Time interval:
\[
\Delta t = 9 - 7 = 2 \text{ months}
\]
Weight gain per month:
\[
\text{Gain per month} = \frac{2.50 \text{ lbs}}{2 \text{ months}} = 1.25 \text{ lbs/month}
\]

Since both intervals yield the same result, we can conclude that the baby gains **1.25 pounds per month** consistently.