A bacteria culture starts with 100 bacteria and doubles in size every half hour.

Question

A bacteria culture starts with 100 bacteria and doubles in size every half hour.
(a) How many bacteria are there after 4 hours?
bacteria

(b) How many bacteria are there after t hours?
y = bacteria

(c) How many bacteria are there after 40 minutes? (Round your answer to the nearest whole number.)
bacteria

(d) Graph the population function.

Explanation / Answer

(a) 1600 (b)at t=1/2 y=200 t=1 y =400 let y = at^2 + b =>200 = a/4 +b =>400 = a+b =>a=800/3,b=400/3 (c) t = 2/3 => y = 800/3*4/9 + 400/3 =>y = 3200/27 + 400/3 =>6800/27 = 251.85 (d) graph is a parabola with equation y = (800/3)*x^2 + 400/3

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