The number of new AIDS cases between 1985 and 1987 if the number of AIDS cases follows

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The number of new AIDS cases between 1985 and 1987 if the number of AIDS cases follows dA/dt = 523.8t2 with initial condition A(0) = 13, 400 and t measured in years since 1981.
Find the change in the state variable between the given times first by solving the differential equation with the given initial conditions and then by using the definite integral.
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