Question

The population of a certain bacteria doubles every 20 minutes. If the initial population were 30 bacilli, how many would there be in 8 hours? (Hint: this is a geometric series)

Answer 1

How many 20 minutes are there in 8 hours?

Answer 2

There are 3 twenty minutes in 1 hour.
There are 24 twenty minutes in 8 hours.

Since the population doubles every 20 minutes, after 24 twenty minutes the population will be 2 x 2 x 2 x ... (24 times) or \(\large 2^{24}\) times the initial population.

Population after 8 hours = \(\large 30 \times 2^{24} \).

You can put it in scientific notation if necessary.