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)?

1 Answer
Aug 8, 2016

~~7514

Explanation:

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