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.

Correct answer:

n =  12

Step-by-step explanation:

$$\begin{gathered} q={\displaystyle \frac{11}{10}}=1.1 \\ {q}^n=3 \\ n\cdot \ln q=\ln 3 \\ {n}_1=\ln (3)\mathrm{/}\ln (q)=\ln (3)\mathrm{/}\ln (1.1)\doteq 11.5267 \\ n=\lceil n_1\rceil =\lceil 11.5267\rceil =12 \end{gathered}$$

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