#### Answer

The number of bacteria the colony will contain after 24 hours is $2.815\times10^{14}$.

#### Work Step by Step

A colony of bacteria has 1 bacterium at start and doubles every half an hour.
We see right away that the rate of change here is $2$ for every half an hour and the starting number of bacteria is $1$.
So, if we take $t$ to be the amount of hours which have passed and $b$ to be the number of bacteria after $t$ hours, we come up with this model to calculate $b$:
$$b=1\times(2)^{2t}$$
$$b=4^t$$
Therefore, after $24$ hours, the number of bacteria in the colony would be
$$b=4^{24}\approx2.815\times10^{14}$$