3. Nancy runs a lemonade stand in her front yard for a week. The table shows the total amount of money she made from her stand [tex]p(d)[/tex] after [tex]d[/tex] number of days. Find [tex]p(6)[/tex] and interpret its meaning.

\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
[tex]$d$[/tex] & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
[tex]$p(d)$[/tex] & 3 & 6 & 9 & 12 & 15 & 18 & 21 \\
\hline
\end{tabular}



Answer :

To solve this problem, let's first understand the table provided. This table shows the total amount of money Nancy made from her lemonade stand over a period of 7 days. The table gives us the values [tex]\( p(d) \)[/tex] for days [tex]\( d \)[/tex] from 1 to 7.

Here's the table again for clarity:

[tex]\[ \begin{array}{|l|c|c|c|c|c|c|c|} \hline d & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline p(d) & 3 & 6 & 9 & 12 & 15 & 18 & 21 \\ \hline \end{array} \][/tex]

To find [tex]\( p(6) \)[/tex], we look at the table value corresponding to [tex]\( d = 6 \)[/tex].

From the table, we see:
[tex]\[ p(6) = 18 \][/tex]

Thus, [tex]\( p(6) \)[/tex] is 18.

Interpreting the meaning of [tex]\( p(6) \)[/tex] in this context:
- [tex]\( p(6) \)[/tex] represents the total amount of money Nancy made after 6 days of running her lemonade stand.
- According to the table, Nancy made a total of 18 dollars after 6 days.

Therefore, [tex]\( p(6) = 18 \)[/tex] means that after 6 days, Nancy's lemonade stand has earned a total of 18 dollars.