Question

The price, p, in dollars, of a stock, t, years after 1999 can be modeled by the function:
p(t) = 0.5t^3 - 5.5t^2 + 14t. When will the price of the stock be more than $90?

Answer 1

so, you want
0.5t^3 - 5.5t^2 + 14t > 90
0.5t^3 - 5.5t^2 + 14t - 90 > 0
1/2 (t-10)(t^2-t+18)
The quadratic factor is always positive, so you just need t > 10

Answer 2

P(t) = 0.5t^3 - 5.5 t^2 + 14t t >$90
P(t) = 0.5t^3 - 5.5 t^2 + 14t - 90 > 0
Using integral zero theorem, possible values of 90 are +/- (1,2,3,5,6,9,10, ...)
P(10) = 0.5 (10)^3 - 5.5(10)^2 + 14 (10) -90 = 0
Therefore, t > 10