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