Microorganisms

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

Result

n =  12

Solution:

q=1110=1.1  qn=3  n⋅ ln⁡q=ln⁡3  n1=ln⁡(3)/ln⁡(q)=ln⁡(3)/ln⁡(1.1)≐11.5267 n=⌈n1⌉=⌈11.5267⌉=12q=\dfrac{ 11 }{ 10 }=1.1 \ \\ \ \\ q^n=3 \ \\ \ \\ n \cdot \ \ln q=\ln 3 \ \\ \ \\ n_{1}=\ln(3)/\ln(q)=\ln(3)/\ln(1.1) \doteq 11.5267 \ \\ n=\lceil n_{1} \rceil=\lceil 11.5267 \rceil=12

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