Question

question 4. the graph shown shows the estimated value, in dollars, of a tablet as a function of the number of months since it was purchased. what is the best interpretation of the y-intercept of the graph in this context?
a. the estimated value of the tablet was $225 when it was purchased.
b. the estimated value of the tablet 24 months after it was purchased was $225.
c. the estimated value of the tablet had decreased by $225 in the 24 months after it was purchased.
d. the estimated value of the tablet decreased by approximately 1.25% each year after it was purch

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a graph is the value of the function when \(x = 0\). In this context, \(x\) represents the number of months since the tablet was purchased, and \(y\) represents the value of the tablet in dollars.

Step2: Analyze each option

• Option A: When \(x = 0\) (the time of purchase), we look at the y - intercept. From the graph, when \(x = 0\), the y - value (value of the tablet) is 225. So this option says the estimated value of the tablet was $225 when it was purchased, which matches the meaning of the y - intercept.
• Option B: When \(x=24\) (24 months after purchase), we look at the value on the graph at \(x = 24\), which is not 225. So this option is incorrect.
• Option C: The y - intercept does not represent the total decrease over 24 months. The decrease over time is shown by the slope (rate of change) of the graph, not the y - intercept. So this option is incorrect.
• Option D: The y - intercept does not give information about the percentage decrease per year. The percentage decrease would be related to the exponential decay (if the graph is exponential) or the slope (if linear), not the y - intercept. So this option is incorrect.

Answer:

A. The estimated value of the tablet was $225 when it was purchased.