A bacteria culture starts with 500 bacteria and doubles in size every 3 hours. How do you find an exponential model for t?

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Answer 1 · 2016-09-28T14:33:28

$B=2^(t/3)(500)$

We start with 500 bacteria, so that is:

$B=500$

At the end of 3 hours, it'll double, so that is:

$B=2xx500=1000$

At the end of another 3 hours, it'll double again, so that is:

$B=2xx2xx500=2^2xx500=2000$

Ok - we've found our exponential. Now to put it into terms that are mathematical and easy to use.

We can write it this way:

$B=2^(t/3)(500)$ - we use $t/3$ so that we can calculate the amount of bacteria even if we have a portion of a 3-hour time period.