The number of bacteria in a culture grew from 275 to 1135 in three hours. How do you find the number of bacteria after 7 hours and Use the exponential growth model: #A = A_0e^(rt)#?

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Answer 1 · 2016-08-08T12:22:03

#~~7514#

#A = A_0e^(rt)#

#t# in hours. #A_0 = 275#. #A(3) = 1135#.

#1135 = 275e^(3r)#

#1135/275 = e^(3r)#

Take natural logs of both sides:

#ln(1135/275) = 3r#

#r = 1/3ln(1135/275)hr^(-1)#

#A(t) = A_0e^(1/3ln(1135/275)t)#

I'm assuming that it's just after 7 hours, not 7 hours following the initial 3.

#A(7) = 275*e^(7/3ln(1135/275)) ~~ 7514#