The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms.

How long will it take for the population of the bacteria to reach 800?

Round your answer to the nearest tenth of an hour.

The answer is 16.3 hours.

Step-by-step explanation:

The population of bacteria in a petri dish doubles every 24 h so it is an exponential growth.

The formula for such growth is P (t) = P (initial) * 2^ (t/24) where t is time in hr.

When the initial population is 500, time to reach 800 is

800=500*2^ (t/24)

2^ (t/24) = 8/5

(t/24) Log (2) = Log (8/5)

t=24*Log (8/5) / Log (2)

=16.27

=16.3 hours

16.3h

Step-by-step explanation:

population 2x in 24 h

going from 500 to 800 is less than double so ans is <24h

solving t: 2^ (t/24) = 800/500

t/24=ln (8/5) / ln2

t=24*ln (8/5) / ln2

=16.3