SOLUTION: For a certain strain of bacteria, k is 0.825 when t is measured in days. How long will it take 20 bacteria to increase to 2000?

Question 138289: For a certain strain of bacteria, k is 0.825 when t is measured in days. How long will it take 20 bacteria to increase to 2000?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For a certain strain of bacteria, k is 0.825 when t is measured in days. How long will it take 20 bacteria to increase to 2000?
:
Let t = number days for 20 to increase to 2000
:
Use the formula:
Ao * 2^(t/k) = A
Where
A = resulting amt, 2000
Ao = initial amt, 20
t = time in days
k = .825
:
20 * 2^(t/.825) = 2000
:
divide both sides by 20 and you have:
2^(t/.825) = 100
:
Use common logs:
log(2^(t/.825)) = log(100)
:
The log equiv of exponents:
(t/.825) * log(2) = log(100)
:
.301(t/.825) = 2
:
Multiply both sides by .825
.301t = .825 * 2
.301t = 1.65
t =
t = 5.482 days
:
:
Check solution on a calc: enter 2^(5.482/.825) * 20 = .2001

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