Question 936075: how do I solve: it takes 12 hrs for a certain bacterial culture to double in size. How long will it take the same bacterial culture to triple?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula is f = p * e^kt
f is the future value
p is the present value
k is the constant of growth or decay
if k is positive, it is the constant of growth.
if k is negative, it is the constant of decay.
t is equal to the time interval.
for it to double, you have the following:
f = 2
p = 1
t = 12 hours
you need to use this equation to solve for k.
formula becomes:
2 = 1 * e^(k*12)
start with:
2 = e^(k*12)
take the natural log of both sides of the equation to get:
ln(2) = ln(e^(k*12))
since ln(e^(k*12)) = k*12*ln(e), and since ln(e) = 1, you get:
ln(2) = k * 12
divide both sides of this equation by 12 to get:
ln(2) / 12 = k
solve for k to get:
k = .057762265
confirm by replacing k in the original equation to confirm that the equation is true.
you get:
2 = 1 * e^(.057762265*12) which becomes 2 = 2.
this confirms the solution for k is good.
now you can use k to solve for how long it will take the same bacterial culture to triple.
equation now becomes:
3 = 1 * e^(.057762265*t)
you are solving for t.
start with:
3 = e^(.057762265*t)
take the natural log of both sides of the equation to get:
ln(3) = ln(e^(.057762265*t) which becomes:
ln(3) = .057762265*t*ln(e) which becomes:
ln(3) = .057762265*t
divide both sides of the equation by .057762265 to get:
ln(3) / .057762265 = t
solve for t to get:
t = 19.01955001
confirm by replacing t in the original equation to see if that equation is true.
original equation is 3 = 1 * e^(.057762265 * 19.01955001) which becomes 3 = 3.
this confirms the solution is correct.
your solution is that it will take 19.01955001 hours for the solution to triple.
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