Question: A population of a colony of bacteria increases by 20% every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am?
My solution: If I want to increase something by 20%, then I would multiply it by (.20). So for the problem above, my solution would be x * (.20) * (.20) = 144000 and I would solve for x. However when I solve for x, the number is 3600000, which doesn't make sense. What exactly am I doing wrong?
If the population increases by $20\%$ every $3$ minutes,
that means it's multiplied by $\color{red}1.20$ every $3$ minutes.