If a virus spreads from 100 computers to 1,000,000 in 120 minutes and the equation is A(base of t)=A(base 0)e^kt , an original virus in 500 computers in 360 minutes?
2006-12-07 02:40:29 · 5 answers · asked by defman88 1 in Science & Mathematics ➔ Mathematics
1000000=100e^120k
e^120k=10000
120k ln e=ln10000
120k=ln 10000
k=ln10000/120
now once k is known the equation is known
plug and chug
2006-12-07 02:45:07 · answer #1 · answered by raj 7 · 0⤊ 0⤋
If a virus spreads from 100 computers to 1,000,000 in 120 minutes then a virus spreads from 1 computer to10,000 computers in 120 minutes.
At = Aoe^kt
10^4 = e^120k
log 10^4 = log e^120k
4= 120k log e
k = 4/(120log e) = 4/(120 * .43429) = .077
At = e^.077*360 =e^27.72
So 500 computers will spread 500e^27.72 viruses in 320 minutes. This is approximately 5.465*10^14 viruses.
2006-12-07 11:27:41 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
You can do the calculation but I will give you a hint.
At time zero, A(t) = 100 = Ao
At time = 120 minute, A(t) = 1000000.
So A(t) = 100*e^k(120) = 1000000.
From this equation, calculate k.
Then in the second case, Ao = 500, t = 360. Use the k you obtain above to calculate A(t).
2006-12-07 10:49:37 · answer #3 · answered by Bruce__MA 5 · 0⤊ 0⤋
I'm guessing you mean 'A sub 0' and 'A sub t' but the rest of the question is lost on me. What are A sub t and A sub 0? Are you looking for the k-value, or what? And what does the last part mean?
Doug
2006-12-07 10:48:17 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
the answer is 2.5657676
i am a teacher
2006-12-07 10:48:12 · answer #5 · answered by clumsy 4 · 0⤊ 0⤋