SOLUTION: During its exponential growth phase, a colony of the bacterium E. color grew from 5067 cells to 39,491 cells in 60 minutes. How long will it take the colony of 5067 cells to grow t

Algebra ->  Finance -> SOLUTION: During its exponential growth phase, a colony of the bacterium E. color grew from 5067 cells to 39,491 cells in 60 minutes. How long will it take the colony of 5067 cells to grow t      Log On


   



Question 1101145: During its exponential growth phase, a colony of the bacterium E. color grew from 5067 cells to 39,491 cells in 60 minutes. How long will it take the colony of 5067 cells to grow to 200,000 cells?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
During its exponential growth phase, a colony of the bacterium E. color grew from 5067 cells to 39,491 cells in 60 minutes.
How long will it take the colony of 5067 cells to grow to 200,000 cells?
let k = the growth constant
the equation
5067%5E%2860k%29+=+38491
using nat logs
ln(5067^60k) = ln(39491)
60k = ln%2839491%29%2Fln%285067%29
60k = 1.2407
k = 1.2407%2F60
k = .020678
:
let m = no. of minutes to reach 200,000 cells
5067%5E%28.020678m%29+=+200000
.020678m = ln%28200000%29%2Fln%285067%29
.020678m = 1.43087
m = 1.43087%2F.020678
m = 69.2 minutes
: