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)A=A0ert?

1 Answer
Aug 8, 2016

~~75147514

Explanation:

A = A_0e^(rt)A=A0ert

tt in hours. A_0 = 275A0=275. A(3) = 1135A(3)=1135.

1135 = 275e^(3r)1135=275e3r

1135/275 = e^(3r)1135275=e3r

Take natural logs of both sides:

ln(1135/275) = 3rln(1135275)=3r

r = 1/3ln(1135/275)hr^(-1)r=13ln(1135275)hr1

A(t) = A_0e^(1/3ln(1135/275)t)A(t)=A0e13ln(1135275)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)) ~~ 7514A(7)=275e73ln(1135275)7514