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)
Device Value 7B2D62
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