Question

The sales of a certain product after an initial release can be found by the function s (t) - 14 4t + 14, where s represents the number of units sold and t represents the time in weeks after release. How many weeks will pass before the product sells approximately 225 units? Round your answer to the nearest week and show your work.

Help would be much appreciated.

Answer 1

The discriminant is negative, there are no real solutions to this equation. This means that the product will never sell approximately 225 units.

Explanation:

We are given the sales function s(t) = -14t^2 + 14t.

We want to find t such that s(t) = 225.

-14t^2 + 14t = 225

Multiplying both sides by -1 and rearranging, we get:

14t^2 - 14t + 225 = 0

We can use the quadratic formula to solve for t:

t = (-(-14) ± sqrt((-14)^2 - 4(14)(225))) / (2(14))

t = (14 ± sqrt(14^2 - 4(14)(225))) / (2(14))

t = (14 ± sqrt(14^2 - 12600)) / 28

t = (14 ± sqrt(196 - 12600)) / 28

t = (14 ± sqrt(-12404)) / 28

Since the discriminant is negative, there are no real solutions to this equation. This means that the product will never sell approximately 225 units.