Bacteria Growth Math Application?

The number N of bacteria present in a culture at time t (in hours) obeys the function N(t) = 1000e^(0.01t).





(a) What is the population of the bacteria after 4 hours?





(b) When will the number of the bacteria reach 1700?





(c) When will the number of bacteria DOUBLE?

Bacteria Growth Math Application?
According to the function you gave,





Total number of bacteria = 1000e^(0.01t) where t is the time (hours).





a) total number of bacteria after 4 hours = 1000e^(0.01*4)


= 1000e^(0.04)





b) 1700 = 1000e^(0.01t)


Ln 1700 = Ln 1000e^(0.01t)


Ln 1700 = Ln 1000 + Ln e^(0.01t)


Ln 1700 = Ln 1000 + 0.01t (Note: Ln e = 1)


t = (Ln 1700 - Ln 1000) / 0.01


t = {Ln (1700/1000) } / 0.01


t = (Ln 1.7) / 0.01





c) double means the bacteria replicate from 1 to 2,from 2 to 4 and so on. So, 2 = 1000e^(0.01t)


0.002 = e^(0.01t)


Ln 0.002 = 0.01t


t = (Ln 0.002) / 0.01
Reply:a)1000e^0.04=1040


b)1700=1000e^0.01t


t=9.5hours


c)2=e^0.01t


t=69.3 hours