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\begin{center}
{\Large Warm-Up Problems and Lecture Problems

February 26, 2003}
\end{center}

\begin{enumerate}


\item  Consider the following initial value problem:
	\[
	\frac{dy}{dt} = \frac{10 - y}{7} \qquad y(0)=21
	\]
	\begin{enumerate}
	\item  Find the \emph{general} solution (i.e., don't take the initial value into account).
		Write you answer as a function of $t$ (i.e., write your answer as $y=$).
	\item  Find the specific solution.
	\end{enumerate}

\newpage

\lecture

\item  In 1980, the population of Nepal was $14.6$ million.
	In 1990, the population was $18.1$ million.
	Let $t$ represent years and let $t=0$ correspond to 1980.
	Find a population model for the population of Nepal:
	\[
	P=P_0e^{kt}
	\]	
	\begin{enumerate}
	\item  Find $P_0$.
	\item  Find $k$.
	\item  Using your model, predict the population in year 1997.
		(The actual population in 1997 was $22.59$ Million.)
	\item  Using your model, predict the population in year 2010.
	\end{enumerate}

\bigskip

\item  (Nearly identical to the previous problem). 
	In 1980, the population of Nepal was $14.6$ million.
	In 1990, the population was $18.1$ million.
	Let $t$ represent years and let $t=0$ correspond to 1900.
	Find a population model for the population of Nepal:
	\[
	P=P_0e^{kt}
	\]	
	\begin{enumerate}
	\item  Find $P_0$ and $k$.
	\item  Using your model, predict the population in year 1997.
		(The actual population in 1997 was $22.59$ Million.)
	\item  Using your model, predict the population in year 2010.
	\end{enumerate}





\end{enumerate}



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