To isolate the variable [tex]\( r \)[/tex] in the equation [tex]\( A = 200(1 + 13r) \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
A = 200(1 + 13r)
\][/tex]
2. Distribute 200 on the right side:
[tex]\[
A = 200 + 2600r
\][/tex]
3. Subtract 200 from both sides to get the term with [tex]\( r \)[/tex] by itself:
[tex]\[
A - 200 = 2600r
\][/tex]
4. Divide both sides by 2600 to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{A - 200}{2600}
\][/tex]
5. Simplify the right-hand side, if possible:
[tex]\[
r = \frac{A}{2600} - \frac{200}{2600}
\][/tex]
[tex]\[
r = \frac{A}{2600} - \frac{1}{13}
\][/tex]
Hence, the rearranged equation isolating [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{A}{2600} - \frac{1}{13}
\][/tex]
The correct answer from the given options is:
[tex]\[
r = \frac{A}{2600} - \frac{1}{13}
\][/tex]
