Itranscript
At 8:00 a.m. the number of bacteria in a jar is recorded. The table below displays the pattern of growth of the bacteria. Note that $t=0$ represents the starting time of $8: 00 \mathrm{a} . \mathrm{m}$.
\begin{tabular}{|c|c|}
\hline Time $t$ (minutes) & Number of Bacteria \\
\hline 0 & 8 \\
\hline 1 & 24 \\
\hline 2 & 72 \\
\hline 3 & 216 \\
\hline$\vdots$ & $\vdots$ \\
\hline
\end{tabular}

Develop a function, $f(t)$, to model the number of bacteria at time $t$.

Step 1 ：The problem provides a table that shows the number of bacteria in a jar at different times. The time $t=0$ represents the starting time of 8:00 a.m. The table is as follows: \begin{tabular}{|c|c|} \hline Time $t$ (minutes) & Number of Bacteria \\ \hline 0 & 8 \\ \hline 1 & 24 \\ \hline 2 & 72 \\ \hline 3 & 216 \\ \hline$\vdots$ & $\vdots$ \\ \hline \end{tabular}

Step 2 ：From the table, it can be observed that the number of bacteria is tripling every minute. At $t=0$, the number of bacteria is 8. At $t=1$, the number of bacteria is 24, which is 3 times the number of bacteria at $t=0$. At $t=2$, the number of bacteria is 72, which is 3 times the number of bacteria at $t=1$. This pattern continues for the given data.

Step 3 ：Therefore, the function $f(t)$ that models the number of bacteria at time $t$ is likely of the form $f(t) = a \cdot 3^t$, where $a$ is the initial number of bacteria.

Step 4 ：Let's use the given data to find the value of $a$. At $t=0$, the number of bacteria is 8, so $f(0) = a \cdot 3^0 = a$. Therefore, $a = 8$.

Step 5 ：So, the function $f(t)$ is $f(t) = 8 \cdot 3^t$.

Step 6 ：\(\boxed{f(t) = 8 \cdot 3^t}\) is the function that models the number of bacteria at time $t$.