clearly, p(t) is exponential
p = a*2^(kt)
at t=0, p=400, so
p(t) = 400*2^(kt)
p(1) = 520, so
400*2^k = 520
k = ln(520/400)/ln2 = 0.3785
At this point, we should really check that the other data points fit this equation, but assuming they do,
(a) p = 400*2^(0.3785t)
(b) t = 1/0.3785 = 2.642 hours
(c) solve 400*2^(0.3785t) = 100000
A population of a given bacteria is noted at the following intervals.
Hours. 0 1. 9. 12. 18
Population. 400. 520. 4242. 9319. 44982
a) Calculate an algebraic model
b) How long does it take for to population to double?
c) When will the population reach 1 000 000?
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