Question

A business has a budget of 2,870 to spend on advertising. Each month, x, the business spends 205 on various advertising. The amount of money remaining in the budget for advertising, a(a), can be described by the function a(x) = -205x + 2870. What is the interpretation of the x-intercept in the context of the problem?

Answer 1

The x-intercept of the function a(x) = -205x + 2870 represents the number of months it takes for the advertising budget to be fully spent, which in this case is 14 months.

Step-by-step explanation:

The x-intercept in a function generally represents the point where the graph of the function crosses the x-axis. In the context of the function a(x) = -205x + 2870, which describes the budget remaining for advertising after spending 205 each month, the x-intercept would indicate the number of months after which the advertising budget would be completely used up. To find the x-intercept, we set the function equal to zero and solve for x:

• 0 = -205x + 2870
• 205x = 2870
• x = 2870 / 205
• x = 14

Therefore, the x-intercept is 14, meaning that the advertising budget will be depleted after 14 months of consistent spending at the rate of 205 per month. This interpretation helps the business plan its advertising strategy and understand the timeline it has before the funds are exhausted.