Algebra word problem

Question

During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 6:00 AM there were 4,000 bacteria present in the culture. At noon the number of bacteria grew to 5,100. How many bacteria will there be at midnight?

Answer 1

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.