SOLUTION: In a certain culture the rate of growth of bacteria is proportional to the amount present. Initially, 1000 bacteria are present and the amount doubles in 12 minutes. Determine the

Algebra ->  Test -> SOLUTION: In a certain culture the rate of growth of bacteria is proportional to the amount present. Initially, 1000 bacteria are present and the amount doubles in 12 minutes. Determine the       Log On


   

Question 948940: In a certain culture the rate of growth of bacteria is proportional to the amount present. Initially, 1000 bacteria are present and the amount doubles in 12 minutes. Determine the time it takes for the bacteria to multiply to 10,000.
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a certain culture the rate of growth of bacteria is proportional to the amount present. Initially, 1000 bacteria are present and the amount doubles in 12 minutes. Determine the time it takes for the bacteria to multiply to 10,000.
--------
y = ab^x
-----
y = 1000*2^(x/12)
-----
Solve::
10,000 = 1000*2^(x/12)
-----
2^(x/12) = 10
----
(x/12) = log(10)/log(2)
x = 12[1/0.3010]
x = 39.86 minutes
====================
Cheers,
Stan H.
--------------

Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
I, initial amount
p, amount after time t
t, time in minutes
"amount doubles in 12 minutes."

The first sentence resembles variation. The second sentence is exponential growth.

p=Ie%5E%28kt%29
Find k.
2000=1000e%5E%28k%2A12%29
2=e%5E%2812k%29
ln%282%29=12%2Ak%2Aln%28e%29
ln%282%29%2F12=k
highlight_green%28k=0.05776%29

How much time from 1000 to 10000?
p=Ie%5E%280.05776%2At%29
10000=1000%2Ae%5E%280.05776t%29
10=e%5E%280.05776t%29
ln%2810%29=0.05776t
t=ln%2810%29%2F0.05776
t=40 minutes.