A bacterium culture initially contains 2000 bacteria and doubles in size every half hour. Find the size of the population after: a) 3 hours b) 80 minutes

Answer 1

At t = 0 (in units of half an hour), y = 1 (in units of 2000 bacteria)

At t = 1, y = 2

At t = 2, y = 4

At t = 3, y = 8

...

Do you see the pattern? What kind of function y(t) would give you these results?

That would be an exponential function (quite topical).

y(t) = a*b^ct, in the units I used above (y(t) = 2^t)

In units of 1 bacterium and t in hours, you have:

y(t) = 2000*2^2t (See that you understand why!)

Solve this for a) t = 3 hours and b) t = 80 minutes = 4/3 hours

a) y(t = 3) = 2000*2^2*3 = 128,000

b) y(t = 4/3) = 2000*2^2*4/3 = 12,699

Answer 2

The exponential growth equation is P = 2000 *2^t/0.5 where t is in hours. Plug in the value of t in hours and evaluate.