Final answer:
The quadratic model y = -11x^2 + 350x is used to predict weekly sales of a product after release, showing initial growth and eventual decline as indicated by the coefficients.
Step-by-step explanation:
The quadratic model given, y = -11x^2 + 350x, represents the sales of a new product x weeks after its release. In the context of the given scenario, the model is used to predict the sales of the product based on the number of weeks since its release. The coefficient of the x^2 term (-11) shows that the sales will decrease over time, while the coefficient of the x term (350) indicates the rate of change in sales.
For example, if we plug in x = 5 into the equation, we can find the sales after 5 weeks. y = -11(5^2) + 350(5) = -11(25) + 1750 = -275 + 1750 = 1475. So, after 5 weeks, the predicted sales would be 1475.
The quadratic model y = -11x^2 + 350x represents the sales (y) of a new product x weeks after its release. The coefficient of x2, which is -11, indicates that the sales growth rate is slowing down over time. The sales initially increased due to the term 350x, suggesting a strong start at the product's release. However, the negative quadratic term suggests that the sales peak and then begin to decline.
This model allows us to predict sales at any given week x and to understand at what point the sales will start to decrease. Furthermore, the model can help the company plan marketing strategies to boost sales before the expected decline.