RimaA300371 RimaA300371
  • 03-11-2022
  • Mathematics
contestada

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

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GraciY559810 GraciY559810
  • 03-11-2022

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]

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