so what's the question?
Do you want N(t) = E(t)?
do you want to know when N(t) stops increasing and starts decreasing?
Do you want to know why E(t) wasn't named S(t)?
The increasing enrollment at Northern High School can be modeled by the equation N(t)= -t^2 + 25t + 600, where t represents the number of years after 2010. The increasing enrollment at Southern High School can be modeled by the equation E(t)= 24t + 570
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