A chef believes that the time it takes to defrost a turkey (`D` hours) varies inversely with the room temperature (`T^\circ \text{C}`). The chef observes that at a room temperature of `20^\circ \text{C}`, it takes 15 hours for the turkey to fully defrost.
- Find the equation relating `D` and `T`. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- By first completing this table of values, graph the relationship between temperature and time. (2 marks)
\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 10\ \ \ & \ \ 15\ \ \ & \ \ \ 20\ \ \ & \ \ \ 25\ \ \ & \ \ \ 30\ \ \ \\
\hline
\rule{0pt}{2.5ex} \ \ D\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ \ & \ \ \ & \ \ \ \ & \ \ \ \ & \ \ \ \\
\hline
\end{array}
--- 0 WORK AREA LINES (style=lined) ---
a. `D \prop 1/T\ \ =>\ \ D=k/T`
| `15` | `=k/20` | |
| `k` | `=15 xx 20=300` |
`:.D=300/T`
b.
\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 10\ \ \ & \ \ 15\ \ \ & \ \ \ 20\ \ \ & \ \ \ 25\ \ \ & \ \ \ 30\ \ \ \\
\hline
\rule{0pt}{2.5ex} \ \ D\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 30\ \ \ & \ \ 20\ \ \ & \ \ \ 15\ \ \ & \ \ \ 12\ \ \ & \ \ \ 10\ \ \ \\
\hline
\end{array}
a. `D \prop 1/T\ \ =>\ \ D=k/T`
| `15` | `=k/20` | |
| `k` | `=15 xx 20=300` |
`:.D=300/T`
b.
\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ D\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 10\ \ \ & \ \ 15\ \ \ & \ \ \ 20\ \ \ & \ \ \ 25\ \ \ & \ \ \ 30\ \ \ \\
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & 30 & 20 & 15 & 12 & 10 \\
\hline
\end{array}