What model describes the relationship between the amount of bacteria and time, given that the bacteria triple every two hours?

1 answer:

3 0

This is exponential. Start with time increments of 1. If we have 4^x, then the bacteria population triples every hour (x=0 -> 1, x=1 -> 4, x=2 -> 16, etc). Now, the problem is that is quadruples every two hours. If you substitute one hour for two, the equation becomes 4^(x/2). (Now at 2 hours, it is 4, at 4 hours, it is 16, ect). I am assuming that the population starts at 1, but it doesn't have to. Let's say the starting population at time 0 is P. Then, the population at time x would be P*4^(x/2). You can verify this for any starting population P>=0 and for any time x>=0.

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