Question 1048271: Solve theproblem using the exponential model and population growth.
-A researcher is investigating a specimen of bacteria. She finds that the original 1000 bacteria grew to 2,048,000 in 60 hours. How fast does the bacteria (a) double? (b) quadruple?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ce^kt=2048000
t=60; C=1000
1000*e^60k=2048000
e^60k=2048=2^11, after dividing by 1000. 1024 is 2^10, and 2048 is 2^11.
ln of both sides
60k=11 ln2
k=11ln2/60=0.1271
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Cd=Ce^(0.1271)t
divide by C, and Cd/C=2, since it is doubling.
2=e^(0.1271)t
ln of both sides
ln2=0.1271 t; ln of e removes it
0.693=0.1271t
t=5.45 hours
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quadruple
ln 4=0.1271t
t=ln4/0.127=10.90 hours, or recognize that doubling twice is quadrupling.
from 1000 to 2048000 is 11 doubling times, and 60/11=5.45
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