Crystal

The crystal grows every month 1.2 permille of its mass. For how many months to grow a crystal from weight 177 g to 384 g?

Correct result:

n =  645.8

Solution:

$$\begin{gathered} q=1+{\displaystyle \frac{1.2}{1000}}=1.0012 \\ {m}_0=177\text{ g } \\ {m}_1=384\text{ g } \\ {m}_1=m_0\cdot q^n \\ {q}^n=m_1\mathrm{/}{m}_0 \\ n\log q=\log (m_1\mathrm{/}{m}_0) \\ n=\log (m_1\mathrm{/}{m}_0)\mathrm{/}\log (q)=\log (384\mathrm{/}177)\mathrm{/}\log (1.0012)=645.8 \end{gathered}$$

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