Calculus - Integrals

The projected rate of increase in enrollment at a new college is estimated by dE/dt = 6,000(t+1)^-3/2 where E(t) is the projected enrollment in t years. If the enrollment is 3,000 now (t=0), find the projected enrollment 15 years from now.

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  1. dE/dt = 6,000(t+1)^-3/2
    E(t) = -12000(t+1)^-1/2 + c
    3000 = -12000+c
    c = 15000

    E(t) = 15000 - 12000/√(t+1)
    E(15) = 15000 - 12000/4 = 12000

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