Question

If 2= (1+ r)^7, solve the equation for r.

Answer 1

`r=\sqrt[7]{2}-1`

Step-by-step explanation:

Given the equation

`2=(1+r)^7`

To solve for r, the first step is to take the 7th root of both sides.

`\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}`

We can simplify further to obtain:

`\begin{gathered} r=1.1040895-1 \\ =0.1040895\text{ (correct to 7 decimal places)} \end{gathered}`