1. **State the problem:** We are given the profit function for a skateboard manufacturer as $$P(x) = 30x - 0.3x^2 - 250$$ where $x$ is the number of skateboards sold. We need to estimate the profit from the sale of the thirtieth skateboard. 2. **Understand the function:** The profit function $P(x)$ gives the total profit from selling $x$ skateboards. To find the profit from the 30th skateboard alone, we calculate the difference in total profit between selling 30 skateboards and 29 skateboards. 3. **Formula used:** The profit from the $n$th skateboard is $$P(n) - P(n-1)$$ 4. **Calculate $P(30)$:** $$P(30) = 30(30) - 0.3(30)^2 - 250 = 900 - 0.3(900) - 250 = 900 - 270 - 250 = 380$$ 5. **Calculate $P(29)$:** $$P(29) = 30(29) - 0.3(29)^2 - 250 = 870 - 0.3(841) - 250 = 870 - 252.3 - 250 = 367.7$$ 6. **Calculate profit from 30th skateboard:** $$P(30) - P(29) = 380 - 367.7 = 12.3$$ 7. **Interpretation:** The profit from selling the 30th skateboard is estimated to be 12.3 units of profit. This method uses the difference in total profit to find the marginal profit from the additional skateboard sold.