A colony of bacteria is grown under ideal conditions in a lab so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. at the end of 5 hours there are 40000. How many bacteria were present initially?

1 Answer
Cesareo R.
May 16, 2016

#6454#

Explanation:

The law of exponential grow is written as
#y = Y_0 e^(alpha t)# where #Y_0# is the initial population
#alpha# the coefficient of exponential grow and #t# time.
When #t=3 times 60 times 60#[s] the population is #10000#
so #10000 = Y_0 e^(alpha 4800)#
and for #t = 5 times 60 times 60#[s] we have
#40000=Y_0 e^(alpha 18000)#
Dividing side by side both equations
#40000/10000 = e^(alpha 15200)->alpha_0 = 0.0000912036#
Now #Y_0=10000/e^(alpha_0 4800) approx 6454 #

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