Math 70 Week 6 Quiz.tex

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 \textsc{Name}
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{\bf Math 70  \\
Quiz 6}
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\item Using the definition of the logarithm function, show that the following equality is true: 
$$ \log(A\cdot B) = \log(A) + \log(B) $$
\vspace{5cm}

\item Expand the following: \\

$\log\left(\frac{3x^2}{y+1}\right)^3$\\

\vspace{1cm}

$\log\sqrt{(x+1)(x+4)}$
\vspace{1cm}

\item Solve for x:\\ 

$10^{3x+ 4} = 10,000$\\

\vspace{1cm}

$ 5^{\frac{x}{2}-1} = 625$
\vspace{1cm}



\newpage
\item How long does it take for \$15,000 to grow to \$50,000 at an 8.5\% annual rate 
compounded continuously?  

\vspace{4cm}









\item
A the amount of a radioactive element left of a sample is given by: 
$$ M(t) = 140e^{-0.031t}$$
Where is $t$ measured in years.  What is the half life of this element?   That
is how long does it take for the sample to decay to half of it's original amount?  

How long does it take for the sample to decay to $\frac{1}{8}$ of it's original amount?




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