Robinson on the island

Robinson Crusoe came to the island with 4 grains of corn. How many years did it take him to grow enough grain for bread if he got 10 grains from one grain on average and he needed at least 1kg of bole for 1 bread, and 1 grain weighs about 0.2g? (assume one harvest per year.)

Correct answer:

x =  4

Step-by-step explanation:

$$\begin{gathered} g_1=4 \\ q=10 \\ {m}_1=1\text{kg}\to \text{g}=1\cdot 1000\text{g}=1000\text{g} \\ {m}_2=0.2\text{g} \\ a=m_1/m_2=1000/0.2=5000 \\ a=g_1\cdot q^x \\ \ln a/g_1=x\ln q \\ {x}_1=\frac{\ln (a/g_1)}{\ln q}=\frac{\ln (5000/4)}{\ln 10}\doteq 3.0969 \\ x=\lceil x_1\rceil =\lceil 3.0969\rceil =4 \end{gathered}$$

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