Calculus

2015-04-11 7:24 pm
A bacteria culture starts with 1,000 bacteria and grows at a rate proportional to its
size. After 2 hours there are 3,000 bacteria. After how many hours will there be
10,000 bacteria?

回答 (2)

2015-04-12 12:50 am
✔ 最佳答案
let P be population and t be hour.

This is a separable equation. Then, it should be easily done.
dP/dt = kP

1/P * dP = k * dt

ln(P) = kt + C

P = C * exp(kt)

Find C when t = 0
1000 = C * exp(0)
C = 1000, which is initial population
P = 1000*exp(kt)

Find k when t=2 and P=3000
3000=1000*exp(k*2)
k=ln(3)/2
k~=.549

Particular solution:
P=1000*exp(.549*t)

Find t.
t=ln(10000/1000)/.549
t=4.19 hours

2015-04-13 05:53:49 補充:
Haha, it' okay. I solved them all based on the tips you gave me.
參考: myself
2015-04-12 7:49 am
Star 唔好意思,可能我又遲了~

加油!

╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯

2015-04-14 16:17:04 補充:
You are so hardworking and brilliant.

Also, you are a morning bird.


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