SOLUTION: Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt. The count in the bacteria culture was 900 after 10 minutes and 1000 after 35 minutes. (a) What

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt. The count in the bacteria culture was 900 after 10 minutes and 1000 after 35 minutes. (a) What       Log On


   

Question 921034: Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt. The count in the bacteria culture was 900 after 10 minutes and 1000 after 35 minutes.
(a) What was the initial size of the culture?


(b) Find the population after 70 minutes.


(c) How many minutes after the start of the experiment will the population reach 11000?


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that the number of bacteria follows an exponential growth model:
P%28t%29=Po%2Ae%5E%28kt%29 where:
P(t) = resulting amt after t time
Po -= initial amt
t = growth period
k = growth constant
:
The count in the bacteria culture was 900 after 10 minutes and 1000 after 35 minutes.
Find k, went from 900 to 1000 in 25 min
900%2Ae%5E%2825k%29+=+1000
e%5E%2825k%29+=+1000%2F900
e%5E%2825k%29+=+10%2F9
using natural logs
25k+=+ln%2810%2F9%29
25k = .10536
k = .10536%2F25
k = .0042

(a) What was the initial size of the culture?
Po%2Ae%5E%28%28.0042%2A35%29%29+=+1000
Po = 1000%2F%28e%5E%28%28.0042%2A35%29%29%29
Po = 863.3 initial size of the culture
:
(b) Find the population after 70 minutes.
P(t) = 863%2Ae%5E%28%28.0042%2A70%29%29
P(t) = 1158 after 70 min
:
(c) How many minutes after the start of the experiment will the population reach 11000?
863%2Ae%5E%28%28.0042t%29%29+=+11000
e%5E%28%28.0042t%29%29+=+11000%2F863
using nat logs
.0042t+=+ln%2811000%2F863%29
.0042t = 2.54523
t = 2.54523%2F.0042
t = 606 minutes to increase to 11000