1. Problem statement: The price of an item is 3000 in the year 2023. The price is expected to increase by 3% per year. We define $x$ as the number of years after 2023 and $p(x)$ as the price of the item $x$ years after 2023. 2. Formula used: For exponential growth, the price after $x$ years is given by $$p(x) = p_0 \times (1 + r)^x$$ where $p_0$ is the initial price and $r$ is the growth rate as a decimal. 3. Applying the values: Here, $p_0 = 3000$ and $r = 0.03$ (3%). So, $$p(x) = 3000 \times (1.03)^x$$ 4. Explanation: This formula means that each year, the price is multiplied by 1.03, representing a 3% increase. After $x$ years, the price grows exponentially according to this formula. Final answer: $$p(x) = 3000 \times (1.03)^x$$