It is given that,
The population of a certain species doubles every nine years.
To write the mathematical expression if the population started with 100 individuals:
According to the condition,
The population of a certain species doubles every nine years.
So that,
[tex]\begin{gathered} 9\text{ years = 1 (In 9 years, it attains the first double)} \\ 1\text{ year = }\frac{1}{9} \\ 2\text{ years = }\frac{2}{9} \\ 3\text{ years = }\frac{3}{9} \\ 4\text{ years = }\frac{4}{9} \\ \text{.}\ldots \\ 9\text{ years = }\frac{9}{9} \\ \text{That is, 1st double} \end{gathered}[/tex]So, In general,
[tex]\frac{t}{9},\text{ where t is number of years.}[/tex]Hence, the mathematical expression is,
[tex]100\times2^{\frac{t}{9}}[/tex]