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A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes,

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A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes,

1.find a formula for the number of bacteria t.

2.find the number of bacteria after one hour.

3.after how many minutes will there be 50 000 bacteria?

Guest Mar 8, 2017
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#1
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Present population =PP

Future population =FP

FP =1,000 x 2^(60/40)

FP =1,000 x 2.828 =2,828 Bacteria after 1 hour.

50,000 = 1,000 x 2^(m/40), where m=minutes

Solve for m over the real numbers:
50000 = 125 2^(m/40 + 3)

50000 = 125 2^(m/40 + 3) is equivalent to 125 2^(m/40 + 3) = 50000:
125 2^(m/40 + 3) = 50000

Divide both sides by 125:
2^(m/40 + 3) = 400

Take the logarithm base 2 of both sides:
m/40 + 3 = (log(400))/(log(2))

Subtract 3 from both sides:
m/40 = (log(400))/(log(2)) - 3

Multiply both sides by 40:
Answer: |m = (40 log(400))/(log(2)) - 120 =225.75 minutes

Guest Mar 8, 2017
#2
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1. N = 1000*(2)^(t/40)      where N is the number after t minutes

2.  After one hour

N = 1000*(2)^(60/40)  ≈ 2828

3.  50000 = 1000*(2)^(t/40)    divide both sides by 1000

50 =  2^(t/40)     take the log of both sides

log (50) = log 2^(t/40)     and we can write

log (50)  = (t/40) * log(2)      divide both sides by log(2)  and multiply by 40

40 * log (50) / log(2)  = t   ≈  225.75 minutes

CPhill  Mar 8, 2017

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