Final Answer:
The effect of advertising on sales can be determined by analyzing the coefficient of the linear term in the sales function. In the given sales function S(t) = 200 + 50t - 5t², the coefficient of the linear term (50t) represents the rate at which sales are increasing per week due to advertising. Therefore, the effect of advertising on sales is a constant increase of 50 units per week.
Explanation:
The sales function is given by S(t) = 200 + 50t - 5t², where t represents the number of weeks after the end of the sales event. To understand the impact of advertising on sales, we look at the coefficient of the linear term (50t). This coefficient indicates the rate of change of sales with respect to time. In this case, the coefficient is positive (50), indicating that the number of units sold increases by 50 units per week due to advertising.
To explain further, the constant term (200) represents the initial sales without advertising, and the quadratic term (-5t²) introduces a decreasing rate of sales growth over time. However, the linear term dominates, leading to a net increase of 50 units per week. This suggests that advertising has a positive and constant effect on sales, contributing to a steady growth of 50 units per week.
In summary, the effect of advertising on sales is a consistent increase of 50 units per week, as indicated by the positive coefficient of the linear term in the sales function. This finding helps the Metro Department Store understand the ongoing impact of advertising on their sales performance.