Answer:
883 bacteria
Step-by-step explanation:
The number of bacteria at noon (12:00 pm) is 180. It increases at a rate of 22% every hour.
At 08:00 pm, 8 hours will have elapsed.
This is a compound interest problem. The final amount of bacteria will be:
[tex]B = P(1 + r)^t[/tex]
where P = initial amount of bacteria = 180
r = rate of increase = 22% = 0.22
t = time elapsed = 8 hours
Therefore:
[tex]B = 180(1 + 0.22)^8\\\\B = 180 (1.22)^8\\\\B = 180 * 4.908[/tex]
[tex]B = 883.44[/tex] ≅ [tex]883[/tex]
There will be 883 bacteria by 8 PM.
