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Mark monitors the growth of a colony of bacteria in his biology lab. He begins with a colony of 100 bacteria. After 24 hours, the colony has grown to 305

bacteria. After 24 more hours, the colony consists of 897 bacteria. What is a reasonable estimate of how many bacteria he can expect to count in the colony

when he returns 24 hours later?

User Nikhil
by
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1 Answer

3 votes

Answer:

After next 24 hours, bacterial population would be
1433

Explanation:

The initial bacterial count at time = 0 was
100

At
= 24 hours, the bacterial count increased up to
305

At
= 48 hours, the bacterial count increased up to
897

As we know that


P = P_0 * e^(rt)

The growth rate of bacterial population is equal to


r = (log(P)/(P_0) )/(t)

Substituting the above values we get -


r = (log(897)/(305) )/(24)\\r = 0. 0195

Count of bacteria after next 24 hours


P = 897 * e^{ 0.0195 * 24)\\P = 1433

User Milt
by
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