Subjects algebra

Device Value 7B2D62

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1. **State the problem:** A customer buys an electronic device for 650. Each year, its value decreases by 39%. We want to determine which statement about the graph of the device's value $y$ over time $x$ years is true. 2. **Model the situation:** The value decreases by 39% each year, so the remaining value each year is $1 - 0.39 = 0.61$ times the previous year's value. 3. **Write the exponential decay formula:** $$y = 650 \times 0.61^x$$ where $x \geq 0$ is years since purchase. 4. **Find the y-intercept:** The y-intercept occurs when $x=0$: $$y = 650 \times 0.61^0 = 650 \times 1 = 650$$ So the y-intercept is 650. 5. **Check for vertical asymptotes:** Exponential decay functions do not have vertical asymptotes. The graph starts at $x=0$ with $y=650$. 6. **Check for horizontal asymptotes:** As $x \to \infty$, $0.61^x \to 0$, so $$y \to 650 \times 0 = 0$$ The horizontal asymptote is $y=0$, not $y=30$. 7. **Conclusion:** The correct statement is (a) The y-intercept of the graph is 650. **Final answer:** (a)