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During a research​ experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 88​:00 AM there were 4 comma 0004,000 bacteria present in the culture. At​ noon, the number of bacteria grew to 4 comma 8004,800. How many bacteria will there be at​ midnight?

Answer :

5100 = 4000e(6r)  .   We want to solve for r; therefore, In(5100/4000) = 6r In(e) = 6r;  therefore, r = .243/6 = .0405. Now plug this value back into the equation for the time from 6am to midnight or 18 hours.  So we have 4000e^(.0405 times 18 hours)  =  8,291.   

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