If you start with $100$ and multiply by $1.05$, what is the new amount? How much more is that than $100$, and is that extra amount a fixed number or a percentage of $100$?

Try writing $1.05$ as $1 + 0.05$. What does that $0.05$ represent compared to the whole (the $1$)? How can you express $0.05$ as a percentage?

Type V(t) = 12000*(1.05)^t into Desmos. Then create a table for this function (for example, with $t = 0, 1, 2$) to see how the account value changes from year to year.

Look at the ratio $V(1)/V(0)$, or in Desmos type V(1)/V(0). Subtract $1$ from this ratio to find the decimal part that represents the increase, then convert that decimal to a percentage and choose the answer choice that describes that yearly percent change.

The function is

This matches the standard exponential form $a(b)^t$, where:

• $a$ is the initial value (starting amount), and
• $b$ is the factor that the amount is multiplied by each time period (here, each year).

The factor $1.05$ tells us how the account changes from one year to the next. Writing it as

shows that each year, the new balance is the old balance plus an additional $0.05$ times the old balance. That extra $0.05$ is a fraction of the current amount, not a fixed dollar amount.

A decimal of $0.05$ corresponds to $5\%$ (because $0.05 = \tfrac{5}{100}$). So multiplying by $1.05$ each year means the account grows by $5\%$ of its current value every year. Among the answer choices, this matches: The account increased by $5\%$ each year.