Answer
a)
[tex]B=B_{0}(1+\frac{a}{12})^{t}[/tex]b)
[tex]B=B_{0}(1+\frac{25}{3}a)^{t}[/tex]c)
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]Explanation
We're given the function:
[tex]B=B_0(1+r)^t[/tex]To represent the equation with the data given in the problem, we need to solve the three parts of this problem.
The part a ask us to write the expression in terms of annual percentage rate (APR) in decimal. If we call "a" the APR in decimal, then the monthly rate is the APR divided in 12:
[tex]r=\frac{a}{12}[/tex]Now we can rewrite the balance equation in terms of the initial investment, the number of months and the APR:
[tex]B=B_0(1+\frac{a}{12})^t[/tex]In part b, we need to write the balance equation using the APR as percentage. The APR as decimal is equal to the APR in percentage divided by 100. If we call A the APR in percentage:
[tex]a=\frac{A}{100}[/tex]Now we replace this value in the balance equation we got in part a:
[tex]B=B_0(1+\frac{100a}{12})^t[/tex]Then simplify:
[tex]B=B_0(1+\frac{25}{3}a)^t[/tex]That's the answer to b.
In part c, we need to write the balance equation with the time in years. Since 1 year has 12 months, if we call the number of months t, and the number of years y:
[tex]t=12y[/tex]Then:
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]And this is the answer to c.