Question150 marks
During an experiment, the number of bacteria in a dish can be modelled by the
where is the number of bacteria, in thousands, and is the time in hours since the start
of the experiment, with .
(i) Complete the table below to show the values of for the given values of .
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline \begin{tabular}{l}
Time, \\
(hours)
\end{tabular} & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline \begin{tabular}{l}
Number of bacteria, \\
(thousands)
\end{tabular} & & & 16 & & 12 & \\
\hline
\end{tabular}
Studdy Solution
STEP 1
1. The function models the number of bacteria in thousands.
2. The time is given in hours and ranges from 0 to 5.
3. We need to calculate for as the values for and are already provided.
STEP 2
1. Calculate for .
2. Calculate for .
3. Calculate for .
4. Calculate for .
STEP 3
Substitute into :
STEP 4
Simplify the expression:
STEP 5
Substitute into :
STEP 6
Simplify the expression:
STEP 7
Substitute into :
STEP 8
Simplify the expression:
STEP 9
Substitute into :
STEP 10
Simplify the expression:
The completed table is:
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