1. **Stating the problem:** We are given the function $$y = 7500 \times \frac{(1.01975)^x - 1}{0.01975}$$ and want to understand its behavior and graph. 2. **Formula explanation:** This function resembles the formula for the sum of a geometric series or a compound interest accumulation formula where the base growth factor is $1.01975$. 3. **Important rules:** - The term $(1.01975)^x$ represents exponential growth. - Subtracting 1 and dividing by $0.01975$ scales the growth appropriately. - Multiplying by 7500 scales the entire function. 4. **Intermediate work:** - The function can be rewritten as $$y = 7500 \times \frac{(1.01975)^x - 1}{0.01975}$$ - For $x=0$, $$y = 7500 \times \frac{1 - 1}{0.01975} = 0$$ - For $x=1$, $$y = 7500 \times \frac{1.01975 - 1}{0.01975} = 7500 \times 1 = 7500$$ 5. **Interpretation:** The function grows exponentially as $x$ increases, starting from 0 at $x=0$ and increasing by a factor related to $1.01975^x$. This function is useful for modeling accumulated growth over time with a fixed growth rate. **Final answer:** The function is $$y = 7500 \times \frac{(1.01975)^x - 1}{0.01975}$$ which models exponential accumulation starting at zero and growing as $x$ increases.