Salman purchased a new laptop for $1,599.00. He expects that it will retain 90% of its value every year. He sketches a graph of the laptops value for the first five years after purchasing it. Which of the following is a key feature of the sketch?

Question

1)the realistic range os from 0 to 1,599
2)the y-intercept is (0,5)
3)the realistic domain is from 0 to 5
4) the graph represents an interesting function.

Answer 1

To analyze the features of the graph representing the value of the laptop over the first 5 years, let's address each option:

1. The realistic range is from 0 to 1,599: This statement is incorrect. The value of the laptop will decrease over time but will not drop below $0. The range would be from \(0\) (the minimum possible value) to \(1,599\) (the initial value).

2. The y-intercept is (0, 5): This statement is incorrect. The y-intercept on the graph will represent the initial value of the laptop when time (years) is 0. Since the laptop costs $1,599, the y-intercept would be (0, 1,599).

3. The realistic domain is from 0 to 5: This statement is correct. The domain represents the time in years after the purchase, which in this case is from \(t = 0\) to \(t = 5\).

4. The graph represents an interesting function: This statement is subjective and might be up for interpretation. The function's interestingness can depend on the context and the viewer's perspective.

Among the given options, the most accurate key feature of the sketch is:

3) the realistic domain is from 0 to 5.