1. **State the problem:** We need to find the new function rule if the total number of questions increases from 250 to 300, but the time frame (number of weeks) remains the same. 2. **Recall the original function:** The original function is given as: $$f(x) = -25(x - 8) + 50$$ where $x$ is the number of weeks elapsed, and $f(x)$ is the number of questions left to submit. 3. **Understand the original parameters:** - The total questions initially: 250 - The slope $a = -25$ means 25 questions are submitted each week. - The function passes through point $(8, 50)$. 4. **Adjust for the new total questions:** If the total questions increase to 300, but the time frame (10 weeks) stays the same, the number of questions submitted per week changes. 5. **Calculate the new slope:** The slope represents the rate of questions submitted per week. Original slope: $$a = \frac{\text{change in questions}}{\text{change in weeks}} = \frac{0 - 250}{10 - 0} = -25$$ New slope: $$a_{new} = \frac{0 - 300}{10 - 0} = -30$$ 6. **Find the new function rule:** Using the point-slope form with the same point $(8, 50)$: $$f_{new}(x) = a_{new}(x - 8) + 50 = -30(x - 8) + 50$$ 7. **Final answer:** $$\boxed{f_{new}(x) = -30(x - 8) + 50}$$ This function represents the number of questions left to submit each week when the total questions increase to 300 over the same 10-week period.