1. **State the problem:** We have the function modeling the number of playgrounds built, $n$, in terms of dollars raised, $r$: $$n = \frac{848r - 1525}{1000}$$ We need to: - (c) Find the inverse function, expressing $r$ in terms of $n$. - (d) Use the inverse to find how many dollars were raised if 39,179 playgrounds were built. 2. **Find the inverse function:** Start with: $$n = \frac{848r - 1525}{1000}$$ Multiply both sides by 1000 to clear the denominator: $$1000n = 848r - 1525$$ Add 1525 to both sides: $$1000n + 1525 = 848r$$ Divide both sides by 848 to solve for $r$: $$r = \frac{1000n + 1525}{848}$$ Show cancellation step: $$r = \frac{\cancel{1000}n + 1525}{\cancel{848}}$$ (This step shows division by 848, no common factors to cancel numerically.) So the inverse function is: $$r(n) = \frac{1000n + 1525}{848}$$ 3. **Calculate dollars raised for $n = 39179$ playgrounds:** Substitute $n = 39179$ into the inverse: $$r = \frac{1000 \times 39179 + 1525}{848}$$ Calculate numerator: $$1000 \times 39179 = 39179000$$ $$39179000 + 1525 = 39180525$$ Divide by 848: $$r = \frac{39180525}{848}$$ Perform the division: $$r \approx 46208.68$$ **Answer:** KaBOOM! raised approximately 46208.68 dollars last year.