The number of bacteria present in a colony is 180 at 12 noon and the bacteria grows at a rate of 22% per hour. how many will be present at 8 p. m. ?
equation:
solution:

Now 12 noon to 8 pm is 8 hours in total, every hour you've increased your bacteria population by 22%
if you start with population P 
after 1 hour we have P*(1+0.22)
after 2 hours we have P*(1+0.22)^2
after 8 hours we have P*(1+0.22)^8
therefore since we started with population 180 at 12 noon we have
at 8 pm, 180*(1+0.22)^2

The principal, real, root of: 50−−√2=7.071067817.07106781−7.0710678150 is not a perfect square