\chapter{Exponentials and logarithms}
\section{Exponential models}
Answer the questions.
\begin{enumerate}
\item
What is the formula for an exponential growth model?
\item
What is the formula for an exponential decay model?
\item
What is the meaning of the constant \(a\) in the exponential model \(f(t)=a e^{kt}\)?
\item
What is the doubling time of an exponential growth model?
\item
What is the half life of an exponential decay model?
\item
What is the formula to relate the constant \(k\) in the exponential model \(f(t)=ae^{-kt}\)
to the half life \(T\)?
\item
In an exponential decay model, we have already found the numerical value of the constant \(k\),
and we now want
to find how long it will take for the quantity to become \(25\%\) of its initial value.
What equation do we need to solve?
\item
In an exponential population growth model with \(t=0\)
corresponding to the year 2004 and initial population \(75,\!000\),
we have found the constant \(k\), and we now want
to find what the population will be in the year 2030.
What do we need to compute?
\end{enumerate}