Crystal

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

Correct result:

n =  645.8

Solution:

q=1+1.21000=1.0012  m0=177 g m1=384 g  m1=m0⋅ qn qn=m1/m0  nlog⁡q=log⁡(m1/m0)  n=log⁡(m1/m0)/log⁡(q)=log⁡(384/177)/log⁡(1.0012)=645.8q=1 + \dfrac{ 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}/m_{0} \ \\ \ \\ n \log q=\log (m_{1}/m_{0}) \ \\ \ \\ n=\log (m_{1}/m_{0}) / \log(q)=\log (384/177) / \log(1.0012)=645.8

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