Hello Colin,

The function $B \left( r \right) = 1000 \left( 1 + r \right)^3$, given in the problem, will give you the total amount of money you would have in the savings account after 3 years depending on the interest rate, $r$. So, this time you are using variables $r$ and $B$, instead of the "usual" $x$ and $y$, where $r$ represents the annual interest rate and $B$ represents the new account balance. (Note: $B\left( r \right) = \dots$ means that they are writing the balance as a function of $r$, same way we usually do $f\left( x \right) = \dots$. It might be easier to think of this expression as just $B = 1000 \left( 1 + r \right)^{3}$).

As it is right now, you would be able to know pretty easily what is the new balance, $B$, if you knew the interest rate, $r$. For part (a) they want you to figure out a formula to do the inverse process, that is, if you knew what the new balance $B$ is, you want to be able to figure out what the interest rate, $r$, was.

Part (b) should be a lot easier to do if you already have part (a). However, if you are still having trouble with part (a), try figuring out first part (b) and then "mimic" the steps you followed there to figure out the formula they want in (a).

Give it another try, and if you are still stuck, let me know what you've already tried and maybe we can figure out what to do next.

Cheers,

David