Answer :
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]
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]
