Mathematics, 21.01.2020 06:31 tylerchitwood211
Abacterial culture starts with 500 bacteria and doubles in size every half-hour.
(a) how many bacteria are there after 3 hours?
since 3 hours equals 6 half-hours, the culture will have doubled 6 times.
therefore, there will be
500 · 2
6 = 32,000
bacteria.
(b) how many bacteria are there after t hours?
since t hours is the same as 2t half-hours, the culture will have doubled 2t
times. therefore, there will be
500 · 2
2t
bacteria.
(c) how many bacteria are there after 40 minutes?
there are two possible answers depending on how you interpret the set-up
to the problem. if each bacterium in the culture doubles once every half-hour on the
half-hour, then each one will double after exactly 30 minutes, and then not again until
60 minutes have passed. in that case, there will be
500 · 2 = 1000
4
bacteria after 40 minutes.
on the other hand, if each bacterium doubles exactly once per half-hour, but at some
random time within that half-hour, then it makes sense to think of the population
function p(t) = 500 · 2
2t as continuous. in that case, since 40 minutes is
40
60
=
2
3
of an hour, the population will be
500 · 2
2
2
3 = 500 · 2
4
3 ≈ 1259
after 40 minutes.
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Abacterial culture starts with 500 bacteria and doubles in size every half-hour.
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(a) how many...
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