%% Math 131, Fall, 2003

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\begin{center}
\textbf{Holy Cross College} \\
\textbf{Math 131 (Professor Hwang), Fall Semester, 2003} \\
Worksheet for Thursday, September~11
\end{center}

Recall that $\clog 2 \simeq 0.30103$ and $\clog 3\simeq0.47712$.

\be

\item Without using a calculator, find $\clog 5$, $\clog 500$, and 
  $\clog 0.5=\clog(1/2)$.

\vfil
\item Without using a calculator, find $\clog 6$, $\clog 12$, and
  $\clog(3/2)$. Verify your answers with a calculator. \\ Hint:
  $6=2\times3$ and $12=2^2\times3$.

\vfil
\item The population of Borduria is given by the formula
  $P=(22.6)(1.035)^t$ million, with $t$~measured in years
  since~1990. In what year will the population reach 40~million?
  
\vfil
\item Referring to the previous question, find the doubling time of
  the population of Borduria, both exactly (as a symbolic answer
  involving logarithms) and numerically.

\vfil
\item The population of a certain species of bacteria triples in one
  hour. How long does it take the population to double in size?

\vfil
\item In this question, you will show that $\clog$~and $\ln$ are
  proportional functions. Start with the equation $y=10^x$, which is
  another way of saying $x=\clog y$. Take the natural logarithm, and
  solve for~$x$. What do you conclude? 
\ee

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