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)
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
+128460 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
