The population p of the city at time t is giv | vedclass

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(B) Given the differential equation: $\frac{dp}{dt} = \frac{p - 200}{2}$.Separating the variables,we get: $\frac{dp}{p - 200} = \frac{1}{2} dt$.Integr

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$200 - 100 e^{t/2}$

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(B) Given the differential equation: $\frac{dp}{dt} = \frac{p - 200}{2}$.Separating the variables,we get: $\frac{dp}{p - 200} = \frac{1}{2} dt$.Integrating both sides: $\int \frac{dp}{p - 200} = \int \frac{1}{2} dt$.This gives: $\ln|p - 200| = \frac{t}{2} + C$.Exponentiating both sides: $p - 200 = e^{t/2 + C} = Ae^{t/2}$,where $A = \pm e^C$.So,$p = 200 + Ae^{t/2}$.Given the initial condition $p(0) = 100$:$100 = 200 + Ae^0 \implies 100 = 200 + A \implies A = -100$.Substituting $A$ back into the equation: $p = 200 - 100 e^{t/2}$.

The population $p$ of the city at time $t$ is given by $\frac{dp}{dt} = \frac{p}{2} - 100$. If the initial population at $t = 0$ is $100$,then $p$ is:

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