### Instruction: The bacteria in a jar triple every 20 seconds. After three minutes, there are 275,562 bacteria in the jar. How many were in the jar at the beginning of the experiment?### Response: I need to find the initial number of bacteria, which I will call x.
I know that the bacteria triple every 20 seconds, so after 20 seconds, there will be 3x bacteria, after another 20 seconds, there will be 3 times 3x, or 9x bacteria, and so on.
I can write this as a general formula: after n 20-second intervals, there will be 3^n times x bacteria.
Three minutes is 180 seconds, so there are 180/20 = 9 intervals of 20 seconds in three minutes.
Therefore, after three minutes, there will be 3^9 times x bacteria.
But I also know that after three minutes, there are 275,562 bacteria.
So I can write an equation: 3^9 times x equals 275,562.
I can simplify this equation by dividing both sides by 3^9, which is 19,683.
So x equals 275,562 divided by 19,683, which is approximately 14.
This means that at the beginning of the experiment, there were 14 bacteria in the jar.