Problem 2
This table shows a linear relationship between the the age of a newborn baby in weeks and their weight.
\begin{tabular}{|c|c|}
\hline age (weeks) & weight (pounds) \\
\hline 1 & 6 \\
\hline 3 & 8 \\
\hline 10 & 15 \\
\hline 12 & 17 \\
\hline
\end{tabular}
Select all the true statements.
A. The weight of the baby increases at a constant rate of 2 lbs every week.
B. The weight of the baby increases at a constant rate of $1 \mathrm{lb}$ every week.
C. The weight of the baby increases at a constant rate of $1 / 2 \mathrm{lb}$ every week.
D. Age is a function of weight.
E. Weight is a function of age.

Step 1 ：First, we need to understand the relationship between the age of the baby in weeks and their weight. From the table, we can see that as the age increases, the weight also increases. This suggests a linear relationship.

Step 2 ：We can calculate the rate of weight increase per week by taking the difference in weight and dividing it by the difference in age. For example, between week 1 and week 3, the weight increases from 6 lbs to 8 lbs, a difference of 2 lbs. The age increases from 1 week to 3 weeks, a difference of 2 weeks. So the rate of weight increase per week is \(\frac{2}{2}=1\) lb per week.

Step 3 ：Similarly, between week 3 and week 10, the weight increases from 8 lbs to 15 lbs, a difference of 7 lbs. The age increases from 3 weeks to 10 weeks, a difference of 7 weeks. So the rate of weight increase per week is \(\frac{7}{7}=1\) lb per week.

Step 4 ：Between week 10 and week 12, the weight increases from 15 lbs to 17 lbs, a difference of 2 lbs. The age increases from 10 weeks to 12 weeks, a difference of 2 weeks. So the rate of weight increase per week is \(\frac{2}{2}=1\) lb per week.

Step 5 ：From the above calculations, we can see that the weight of the baby increases at a constant rate of 1 lb every week. So statement B is true.

Step 6 ：Since the weight of the baby does not increase at a constant rate of 2 lbs every week or 1/2 lb every week, statements A and C are false.

Step 7 ：Since the weight of the baby increases as the age increases, we can say that the weight is a function of age. So statement E is true.

Step 8 ：However, the age is not a function of weight because for a given weight, there could be multiple corresponding ages. So statement D is false.

Step 9 ：Finally, we check our results and find that they meet the requirements of the problem. So the true statements are B and E.

Step 10 ：\(\boxed{\text{The true statements are B and E.}}\)