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(Solved): The population $$P$$ (in thousands) of a country can be modeled by $P=-14.75 t^{2}+788.5 t+117, ... The population $$P$$ (in thousands) of a country can be modeled by \[ P=-14.75 t^{2}+788.5 t+117,228$ where $$t$$ is time in years, with $$t=0$$ corresponding to 1980 . (a) Evaluate $$P$$ for $$t=0,10,15,20$$, and 25. $$\begin{array}{ll}P(0)= & \text { thousand people } \\ P(10)= & \text { thousand people } \\ P(15)= & \text { thousand people } \\ P(20)= & \text { thousand people } \\ P(25)= & \text { thousand people }\end{array}$$ Explain these values. The is (b) Determine the population growth rate, $$d P / d t$$. $\frac{d P}{d t}=$ (c) Evaluate $$d P / d t$$ for the same values as in part (a). \begin{aligned} P^{\prime}(0)= & \text { thousand people per year } \\ P^{\prime}(10)= & \text { thousand people per year } \\ P^{\prime}(15)= & \text { thousand people per year } \\ P^{\prime}(20)= & \text { thousand people per year } \\ P^{\prime}(25)= & \text { thousand people per year } \end{aligned} Explain your results. The is

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