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A given bacteria culture initially contains 2500 bacteria and doubles every half hour. The number of bacteria p at a given time t is given by the formula p(t)=2500ekt for some constant k. (You will need to find k to answer the following.) (a) Find the size of the bacterial population after 50 minutes. (b) Find the size of the bacterial population after 8 hours.



Answer :

Giovi
After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:
[tex]5000=2500 e^{30k} [/tex]
and:
[tex] e^{30t}= \frac{5000}{2500}=2 [/tex]
Apply the natural logarithm ln to both sides and get:
[tex]30t=ln(2)[/tex]
so [tex]k=0.0231 [/tex] in units of [tex] \frac{1}{min} [/tex]
so your equation is now:
[tex]p(t)=2500 e^{0.0231t} [/tex]
1] it t= 50 min substituting you get:
[tex]p(50)=2500 e^{0.0231*50}=7935 [/tex] bacteria
2] if t= 8 h = 480 min you get:
[tex]p(480)=2500 e^{0.0231*480}=1.6* 10^{8} [/tex] bacteria

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