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Consider the following problem:$\newline$The number of people in a cafeteria is changing at a rate of $r(t)=1920-160 t$ people per hour (where $t$ is the time in hours). At time $t=11.5$, there were $60$ people in the cafeteria. How many people were in the cafeteria at hour $12$.$5$ ?$\newline$Which expression can we use to solve the problem?$\newline$Choose $1$ answer:$\newline$(A) $\int_{11.5}^{12.5} r^{\prime}(t) d t$$\newline$(B) $60+\int_{11.5}^{12.5} r^{\prime}(t) d t$$\newline$(C) $\int_{11.5}^{12.5} r(t) d t$$\newline$(D) $60+\int_{11.5}^{12.5} r(t) d t$