The wrong strain of the bacterium escherichia coli can be...

The wrong strain of the bacterium Escherichia coli can be dangerous if you ingest it, but other strains are common model organisms in the lab. E. coli are about 2 micrometers long. By contrast, a human neuron that reaches all the way from your brain down to your leg might be a meter long.

Escherichia coli (E. coli) is a bacterium that can reproduce at an exponential rate. The $E$ coli reproduce by dividing. A small number of E. coli bacteria in the large intestine of a human can trigger a serious infection within a few hours. Consider a particular E. coli infection that starts with $100 E .$ coli bacteria. Each bacterium splits into two parts every half hour. Assuming none of the bacteria die, the size of the $E .$ coli population after $t$ hours is given by $P(t)=100 \cdot 2^{2 t},$ where $0 \leq t \leq 16$ a. Find $P(3)$ and $P(6)$ b. Use a graphing utility to find the time, to the nearest tenth of an hour, it takes for the $E .$ coli population to number 1 billion.