The first generation of microorganisms has a population of 13500 members. Each subsequent generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.

Correct answer:

n =  13

Step-by-step explanation:

q=1011=1.1  qn1 = 3  (n1)   ln q = ln 3  n1=ln3/lnq+1=ln3/ln1.1+112.5267 n=n1=12.5267=13   Verifying Solution:  a1=1 a2=a1 q=1 1011=101 11=1011=1.1 a3=a2 q=1011 1011=10 1011 11=100121=1.21 a4=a3 q=100121 1011=100 10121 11=10001331=1.331 a5=a4 q=1.331 1.1=1.4641 a6=a5 q=1.4641 1.11.6105 a7=a6 q=1.6105 1.11.7716 a8=a7 q=1.7716 1.11.9487 a9=a8 q=1.9487 1.12.1436 a10=a9 q=2.1436 1.12.3579 a11=a10 q=2.3579 1.12.5937 a12=a11 q=2.5937 1.12.8531 a13=a12 q=2.8531 1.13.1384

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