Question

A population of rabbits is growing exponentially! In just 5 weeks it goes from a population of 100 to 1000. What is the doubling time of this population? As in, how long does the population take to double?

Answer 1

which formula do you use in order to model the exponential growth?

Answer 2

since there are more than one formula

Answer 3

we can use this formula:
\[\huge N = A{e^{Bt}}\]
where \(A, \;B\) are two numeric constants
Now using data you provided, we have:
\[\huge \left\{ \begin{gathered}
100 = A \hfill \\
1000 = A{e^{5B}} \hfill \\
\end{gathered} \right.\]
the solution of such system is:
\[\huge A = 100,\quad B = 0.46\]

Answer 4

Let's suppose that at week \(\tau\), the number of rabbits, is 200, then, in order to answer to your question, we have to solve such equation:
\[\huge 200 = 100 \cdot {e^{0.46 \cdot \tau }}\]