The balance oif a savings account can be modeled by the function b(t)=5000(1.024)^t, where t is the time in years, To model the monthly balance, a student writes:

Question

b(t)=5000(1.024)^t = 5000(1.024)^(1/12 * 12)^t = 5000(1.024^1/12)^12t = 5000(1.002)^12t

Is the student correct? Explain your reasoning.