To prevent an epidemic, the Health Department of a city disinfected all neighborhoods to prevent the spread of the dengue mosquito. It is known that the number $f$ of infected people is given by the function $f(t) = -2t^{2} + 120t$ (where $t$ is expressed in days and $t = 0$ is the day before the first infection) and that this expression is valid for the first 60 days of the epidemic. The Health Department decided that a second disinfection should be done on the day when the number of infected people reached 1600 people, and a second disinfection had to take place. The second disinfection began on (A) the $19^{\text{th}}$ day. (B) the $20^{\text{th}}$ day. (C) the $29^{\text{th}}$ day. (D) the $30^{\text{th}}$ day. (E) the $60^{\text{th}}$ day.
To prevent an epidemic, the Health Department of a city disinfected all neighborhoods to prevent the spread of the dengue mosquito. It is known that the number $f$ of infected people is given by the function $f(t) = -2t^{2} + 120t$ (where $t$ is expressed in days and $t = 0$ is the day before the first infection) and that this expression is valid for the first 60 days of the epidemic.
The Health Department decided that a second disinfection should be done on the day when the number of infected people reached 1600 people, and a second disinfection had to take place.
The second disinfection began on
(A) the $19^{\text{th}}$ day.
(B) the $20^{\text{th}}$ day.
(C) the $29^{\text{th}}$ day.
(D) the $30^{\text{th}}$ day.
(E) the $60^{\text{th}}$ day.