Answer:
[tex]r=\sqrt[7]{2}-1[/tex]Explanation:
Given the equation
[tex]2=(1+r)^7[/tex]To solve for r, the first step is to take the 7th root of both sides.
[tex]\begin{gathered} \sqrt[7]{2}=\sqrt[7]{(1+r)^7} \\ 1+r=\sqrt[7]{2} \\ \text{Therefore the exact value of r is:} \\ r=\sqrt[7]{2}-1 \end{gathered}[/tex]We can simplify further to obtain:
[tex]\begin{gathered} r=1.1040895-1 \\ =0.1040895\text{ (correct to 7 decimal places)} \end{gathered}[/tex]