Final answer:
The cumulative number of cases of Senioritis can be modeled by a quadratic regression equation. To estimate when 200 Senioritis cases had been diagnosed, substitute S(x) = 200 in the equation and solve for x. The approximate years when 200 Senioritis cases were diagnosed are 2001 and 2005.
Step-by-step explanation:
The given equation S(x) = - 30x^2 + 180x + 64 is a quadratic regression equation. To estimate when 200 Senioritis cases had been diagnosed, we need to find the value of x when S(x) is equal to 200. So, we substitute S(x) = 200 in the equation and solve for x.
-30x^2 + 180x + 64 = 200
-30x^2 + 180x - 136 = 0
Using the quadratic formula, x = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -30, b = 180, and c = -136.
By solving the equation, we find that x = 1 or x ≈ 4.8. Since x represents the number of years after 2000, we can conclude that 200 Senioritis cases were diagnosed around the year 2001 or approximately 2005.