A colony of bacteria

Nicci
student

Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain at the end of 50 hours?

Hi Nicci,

I think that you should first calculate what happens for the first few hours. I would keep track in a table.

Time (hours)	Population
0	1
1/2	2
1	4
1 1/2	8
2	16
2 1/2	32
3	64

Notice that the numbers in the "Population" column are all powers of 2. I am going to use this fact and the doubling period is one half hour to rewrite the table.

Number of doubling time periods	Population
0	1 = 2⁰
1	2 = 2¹
2	4 = 2²
3	8 = 2³
4	16 = 2⁴
5	32 = 2⁵
6	64 = 2⁶

Now can you see what the population would be after 50 hours?

Cheers,
Penny Go to Math Central