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Q giken,rate of growthy=200 t e^{-0.5 t}To Find totu infated peupie\int y d t \int_{0}^{\infty} 200 t e^{-0.5 t} d tI=\int_{0}^{\infty} 200 t e^{-0 i t} d tintegsating by \int u v methed\begin{array}{l}I=\int_{0}^{\infty} 200\left[t \int e^{-0.5 t} \partial t-\int\left(\frac{\partial t}{\partial t} \int e^{-0.5 t} d t\right)\right. \\I=200\left[t \frac{e^{-0.5 t}}{-0.5}-\left(\frac{e^{-0.5}}{-0.5}\right) d t\right. \\I=200\left[-2 t \int_{0}^{\infty}\left[e^{-0.5 t}(0.5)^{2}\right.\right. \\I=200.0(-2)\left(\frac{t}{e^{-0.5 t}}\left(2 e^{-0.5 t}\right)_{0}^{\infty}\right.\end{array}I=-400\frac{t}{e^{0.5 t}}<1 a^{v^{0 v^{5}}} su c t=\infty\frac{t}{e^{0} \text { st }} will be zelo.\begin{array}{l}I=-400\left(0+\frac{2}{e^{\infty}}(0+2)\right) \\\Rightarrow I=800 \\I\end{array} ...