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.
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?
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