The sales of new products over time are found to follow a quadratic model before dropping off to zero at the end of the product’s lifetime. A new product is released with sales modeled by the equation S=−(t−3)^2+81, where S represents the sales in millions of dollars and t represents the number of years the product will be sold. According to the equation, what will be the lifetime of this product?

1 answer

To find the lifetime of the product, we need to determine the value of t when the sales, S, drop to zero.

Set S=0 in the equation:

0 = -(t-3)^2 + 81

-(t-3)^2 = -81

(t-3)^2 = 81

Taking the square root of both sides:

t-3 = ±√81
t-3 = ±9

t = 3 + 9 or t = 3 - 9

t = 12 or t = -6

Since the product cannot be sold for a negative number of years, the lifetime of the product is 12 years.