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Consider the following problem:$\newline$The number of people in Bernardo's social network is increasing at a rate of $r(t)=-2(t-3)^{2}+23$ people per month (where $t$ is the time in months since Bernardo set up the network). At time $t=4$ months, Bernardo had $80$ people in his social network. How many people were in Bernardo's social network at the end of the $6^{\text {th }}$ month?$\newline$Which expression can we use to solve the problem?$\newline$Choose $1$ answer:$\newline$(A) $r(6)$$\newline$(B) $80+\int_{4}^{6} r(t) d t$$\newline$(C) $\int_{4}^{6} r(t) d t$$\newline$(D) $\int_{0}^{6} r(t) d t$