1. **State the problem:** We need to find the Instantaneous Rate of Change (IROC) of the function $$y = 4\sqrt{100} - 2t$$ at $$t = 15$$ without using derivatives. 2. **Rewrite the function:** Note that $$\sqrt{100} = 10$$, so the function simplifies to: $$y = 4 \times 10 - 2t = 40 - 2t$$ 3. **Understand IROC without derivatives:** The IROC at a point can be approximated by the average rate of change over a very small interval around that point: $$\text{IROC at } t = 15 \approx \frac{y(15 + h) - y(15)}{(15 + h) - 15} = \frac{y(15 + h) - y(15)}{h}$$ where $$h$$ is a very small number. 4. **Calculate values:** - $$y(15) = 40 - 2 \times 15 = 40 - 30 = 10$$ - $$y(15 + h) = 40 - 2(15 + h) = 40 - 30 - 2h = 10 - 2h$$ 5. **Calculate the difference quotient:** $$\frac{y(15 + h) - y(15)}{h} = \frac{(10 - 2h) - 10}{h} = \frac{-2h}{h}$$ 6. **Simplify by canceling $$h$$:** $$\frac{\cancel{-2h}}{\cancel{h}} = -2$$ 7. **Interpretation:** As $$h \to 0$$, the average rate of change approaches $$-2$$, so the IROC at $$t = 15$$ is: $$\boxed{-2}$$ This means the function decreases by 2 units in $$y$$ for every 1 unit increase in $$t$$ at $$t=15$$.