Which expression represents the number of cells after half...

Which expression represents the number of cells after half an hour? A $2^{10}$ B $2^{15}$ C $2^{20}$ D $2^{30}$ $$\begin{array}{|c|c|} \hline \begin{array}{c} \text { Time } \\ \text { (min) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Bacteria } \end{array} \\ \hline 0 & 2^{0} \\ \hline 3 & 2^{1} \\ \hline 6 & 2^{2} \\ \hline 9 & 2^{3} \\ \hline 12 & 2^{4} \\ \hline \end{array}$$

Which expression represents the number of cells after half an hour?
A $2^{10}$
B $2^{15}$
C $2^{20}$
D $2^{30}$
$$\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Time } \\
\text { (min) }
\end{array} & \begin{array}{c}
\text { Number of } \\
\text { Bacteria }
\end{array} \\
\hline 0 & 2^{0} \\
\hline 3 & 2^{1} \\
\hline 6 & 2^{2} \\
\hline 9 & 2^{3} \\
\hline 12 & 2^{4} \\
\hline
\end{array}$$

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Key Concepts

Exponential Growth

Exponential growth refers to an increase in quantity where the rate of growth is proportional to the current amount. This concept is inherent in situations where a quantity doubles or multiplies by a constant factor over fixed intervals, leading to a rapid increase in size over time.

Doubling Time

Doubling time is the period over which a quantity experiencing exponential growth multiples to twice its previous amount. Understanding doubling time is essential in modelling processes like cell division, where the number of entities doubles at each interval.

Exponential Function Notation

Exponential function notation, often written as a^n for some base a and exponent n, efficiently represents repeated multiplication. It is a compact way to denote how many times a quantity is scaled, commonly used to describe phenomena such as bacterial cell division.

Discrete Time Intervals

Discrete time intervals involve breaking up a continuous process into separate, countable units of time. This approach allows for the analysis of growth processes at specific moments, such as every few minutes in a biological context.

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