Alisa buys a watermelon every year. The first time she bought a watermelon, in Year 0, it cost $2.50. She notices the price is getting more expensive, at a rate of 3% per year.
Alisa sketches a graph of the situation.
Which statements are true?
Select each correct answer.
The graph has an x-intercept and a y-intercept.
The graph has a y-intercept but no x-intercept.
The graph decreases from left to right.
The point (0, 2.50) is on the graph.
The point , , , begin ordered pair 0 comma 2.50 end ordered pair, , , is on the graph.
The point (2.50, 0) is on the graph.
To answer this question, let's analyze the information provided.
We know that Alisa buys a watermelon every year, starting from Year 0. The cost of the watermelon in Year 0 is $2.50, and the price increases by 3% each year. This means that the price of the watermelon in Year 1 would be:
$2.50 + ($2.50 * 0.03) = $2.50 + $0.075 = $2.575
Similarly, we can find the price of the watermelon in subsequent years. Now, let's interpret this information and analyze the options given.
1. The graph has an x-intercept and a y-intercept: This statement is FALSE. An x-intercept is a point where the graph intersects the x-axis (y-coordinate is zero), and a y-intercept is a point where the graph intersects the y-axis (x-coordinate is zero). In this case, since the watermelon's price increases every year, the graph will never intersect the x-axis (the price will never be zero), so there are no x-intercepts. However, it does have a negative y-intercept since the initial cost of the watermelon in Year 0 is $2.50.
2. The graph has a y-intercept but no x-intercept: This statement is TRUE. As explained above, the graph has a y-intercept at the point (0, 2.50). This represents the cost of the watermelon in Year 0.
3. The graph decreases from left to right: This statement is FALSE. Since the price of the watermelon increases every year, the graph will always move upwards from left to right.
4. The point (0, 2.50) is on the graph: This statement is TRUE. As explained above, (0, 2.50) represents the cost of the watermelon in Year 0.
5. The point (2.50, 0) is on the graph: This statement is FALSE. Since the x-coordinate represents the year and the y-coordinate represents the price, the point (2.50, 0) does not make sense in this context. The price will never be zero unless it's a negative value, which doesn't apply to this situation.
Based on the explanations above, the correct statements are:
- The graph has a y-intercept but no x-intercept.
- The point (0, 2.50) is on the graph.