A certain bacteria doubles its population every 12 hours. After 3 days, there were 1,600 bacteria. How many bacteria were there at the beginning of the first day?

We start with some practical thinking. if there are 24 hours in a day, and the time span we are given is 3 days, then we know that the amount of time the bacteria has doubled is 72 hours. We then look at the rate at which the bacteria multiply, we are told every 12 hours. 72 hours (total incubation period), divided by 12 hours (the amount of time needed for multiplication to occur) gives us a total of 6 instances of the bacteria doubling. Stay with me.

Knowing that something doubles means that it is multiplied by two. As we saw above, the original number of bacteria (or b in the coming equation) doubled 6 times. To solve, we would say that b x 26 [2 to the 6th power is simpler than saying 2x2x2x2x2x2] = 1600 [the total amount after 3 days. Isolating b gives us 1600/26 = 25. So the amount of bacteria in the culture originally was 25. We can check the work by multiplying 25 * 2 * 2 * 2 * 2 * 2 * 2, which gives us the final amount of 1600 after 3 days (72 hours).

Step-by-step explanation: