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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?

 

please answer has soon as possible .(due tomorrow)

Guest Mar 8, 2017
 #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

 

 

cool cool cool

CPhill  Mar 8, 2017

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