Well digging cost

Mr. Peter needs to dig a 20 m deep well on his property. The AZET company charges 1 euro for the first meter and 2x more for each subsequent meter. The ZETA company charges 200 euros for each meter of well depth. Which company should Mr. Peter choose if he wants to save as much as possible?

Final Answer:

x = ZETA

Step-by-step explanation:

$$\begin{gathered} h=20\text{m} \\ q=2\text{Eur/m} \\ {a}_1=1\text{m} \\ n=h/1=20/1=20 \\ {c}_1=a_1\cdot \frac{q^n-1}{q-1}=1\cdot \frac{2^{20}-1}{2-1}=1048575\text{Eur} \\ {c}_2=n\cdot 200=20\cdot 200=4000\text{Eur} \\ {c}_2<c_1 \\ x=ZETA \end{gathered}$$

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