To find the cost of a liter of milk for the years 2007 and 2008 considering the given inflation rates, we approach the problem step-by-step.
Step 1: Understand the Given Data
1. Cost of milk in 2006: [tex]\( R 4.45 \)[/tex]
2. Inflation rate for 2007: [tex]\( 6.5\% \)[/tex] (or [tex]\( 0.065 \)[/tex] in decimal form)
3. Inflation rate for 2008: [tex]\( 11.5\% \)[/tex] (or [tex]\( 0.115 \)[/tex] in decimal form)
4. Cost of a cold drink in 2006: [tex]\( R 5.99 \)[/tex]
Step 2: Calculate the Cost of Milk in 2007
To find the cost of milk in 2007, we need to account for the 2007 inflation rate:
[tex]\[ \text{Cost of Milk in 2007} = \text{Cost of Milk in 2006} \times (1 + \text{Inflation Rate for 2007}) \][/tex]
[tex]\[ \text{Cost of Milk in 2007} = 4.45 \times (1 + 0.065) \][/tex]
Let's break this down:
[tex]\[ = 4.45 \times 1.065 \][/tex]
[tex]\[ = 4.73925 \][/tex]
So, the cost of milk in 2007 is [tex]\( R 4.73925 \)[/tex].
Step 3: Calculate the Cost of Milk in 2008
To find the cost of milk in 2008, we use the cost of milk in 2007 and account for the 2008 inflation rate:
[tex]\[ \text{Cost of Milk in 2008} = \text{Cost of Milk in 2007} \times (1 + \text{Inflation Rate for 2008}) \][/tex]
[tex]\[ \text{Cost of Milk in 2008} = 4.73925 \times (1 + 0.115) \][/tex]
Let's break this down:
[tex]\[ = 4.73925 \times 1.115 \][/tex]
[tex]\[ = 5.28426375 \][/tex]
So, the cost of milk in 2008 is [tex]\( R 5.28426375 \)[/tex].
Step 4: Complete the Table
Now that we have calculated the costs for 2007 and 2008, we can fill in the table:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
\textbf{Average Rate} & \textbf{2006} & \textbf{2007} & \textbf{2008} \\
\hline
\begin{tabular}{l}
\textbf{Cost of a litre of} \\
\textbf{milk}
\end{tabular} & R 4.45 & R 4.73925 & R 5.28426375 \\
\hline
\begin{tabular}{l}
\textbf{Cost of a litre of} \\
\textbf{cold drink}
\end{tabular} & R 5.99 & & \\
\hline
\end{tabular}
\][/tex]
So, after considering the inflation rates for 2007 and 2008, the updated table would look like this:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
\textbf{Average Rate} & \textbf{2006} & \textbf{2007} & \textbf{2008} \\
\hline
\begin{tabular}{l}
\textbf{Cost of a litre of} \\
\textbf{milk}
\end{tabular} & \textbf{R 4.45} & \textbf{R 4.73925} & \textbf{R 5.28426375} \\
\hline
\begin{tabular}{l}
\textbf{Cost of a litre of} \\
\textbf{cold drink}
\end{tabular} & \textbf{R 5.99} & & \\
\hline
\end{tabular}
\][/tex]
