The percentage increase each year is $10$%, so at the end of the year you will have $110$% of the value at its start. This corresponds to a multiplier of $1.1$.

After one year, it is worth: $$2000 \times 1.1 = $$$2200$

After two years it is worth: $$2000 \times 1.1^2 = $$$2420$

After three years it is worth: $$2000 \times 1.1^3 = $$$2662$

This suggests that if the investment is left for $n$ years it would be $$2000 \times 1.1^{n}$.

Observe that:

\( \begin{align} \displaystyle u_{0} &= \$2000 &\text{initial investment}\\ u_{1} &= \$2000 \times 1.1 &\text{amount after 1 year}\\ u_{2} &= \$2000 \times 1.1^2 &\text{amount after 2 years}\\ u_{3} &= \$2000 \times 1.1^3 &\text{amount after 3 years}\\ u_{4} &= \$2000 \times 1.1^4 &\text{amount after 4 years}\\ \vdots \\ u_{n} &= \$2000 \times 1.1^n &\text{amount after } n \text{years}\\ \end{align} \)