A bacteria culture starts with 2000 bacteria and the population doubles after 2 hrs. If we express the number of bacteria after t hours as y(t)=a(e^kt) find a and k

Answer 1

y=ae^kt, where t is time; usually t ≥ 0.

The initial number of bacteria is 2000. That means when t = 0, y = 2000.

2000 = ae⁰

2000 = a ("a" is the initial value for the exponential function; this will be the case unless the function has a horizontal or vertical shift).

y = 2000e^kt; we know that after 2 hours (t = 2) the bacterial population has doubled to 4000).

4000 = 2000e^2k

2 = e^2k

ln(2) = ln(e^2k)

ln(2) = 2kln(e)

ln(2) = 2k

k = (1/2)ln(2) or ln(√2) ≈ 0.34657

So,

y(t) = 2000e^0.34567t

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