Ideal Under
Under ideal conditions a certain bacteria population is known to double every two hours. ?
Under ideal conditions a certain bacteria population is known to double every two hours. Suppose there are initially 100 bacteria.
What is the size of the population after t hours?
thanks for any and all help!
Equations of this type are of the form:
dx/dt=kx
dx/x=kdt
dx/dt is the rate of population change with respect to time. k is a growth constant
the solution to this is
lnx=kt+C
x=e^(kt+c)
x=Ce^kt
C=e^c, which is constant. It’s the initial population. Since the population doubles every 2 hours, we can solve for k by plugging in 2 and setting the equation equal to 200.
200=100e^2k
2=e^2k
ln2=2k
k=(1/2)ln2
=ln(sqrt(2))
So the model for these bacteria is:
P=100e^(ln(sqrt(2))t
We can simplify this by seperating ln2 and t
P=100(e^ln(sqrt(2))^t
P=100*(sqrt(2))^t
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