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# A bacteria culture starts with 1,000 bacteria and doubles in size every 3 hours. Find an exponential model for the size of the culture as a function of time t in hours and use the model to predict how many bacteria there will be after 2 days.

Solution

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A quantity $y$ experiences exponential growth if

$y=Ab^{t}$ with $b>1$.

We are given:

$\left\{\begin{array}{ll} 1000=Ab^{0} & \text{ (... when t = 0 hours )}\\ 2000=A\cdot b^{3} & \text{ (... doubles for t = 3)} \end{array}\right.$

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