The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.
<h3>What is the equivalent expression?</h3>
Based on the expression given, Carmen's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^nm
- FV = Future value
- P = Present value
- R = interest rate
- m = number of compounding
- N = number of years
5000(1.0005)^12t
= 5000(1.0005^12)^t
50002.5^12t
Please find attached the complete question.To learn more about future value, please check: brainly.com/question/18760477
Step 1. Divide both side by 16
100/16 = 6t - 13
Step 2. Dimplify 200/16 to 25/2
25/2 = 6t - 13
Step 3. Add 13 to both sides
25/2 + 13 = 6t
Step 4. Simplify 25/2 + 13 to 51/2
51/2 = 6t
Step 5. Divide both sides by 6
51/2/6 = t
Step 6. Simplify 51/2/6 to 51/2 * 6
51/2 * 6 = t
Step 7. Simplify 2 * 6 to 12
51/12 = t
Step 8. Simplify 51/12 to 17/4
17/4 = t
Step 9. Switch sides
t = 17/4