Question

under ideal conditions, the population of a certain species doubles every nine years. If the population started with 100 individuals, write the mathmatical expression.

Answer 1

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,

`\begin{gathered} 9\text{ years = 1 (In 9 years, it attains the first double)} \\ 1\text{ year = }(1)/(9) \\ 2\text{ years = }(2)/(9) \\ 3\text{ years = }(3)/(9) \\ 4\text{ years = }(4)/(9) \\ \text{.}\ldots \\ 9\text{ years = }(9)/(9) \\ \text{That is, 1st double} \end{gathered}`

So, In general,

`(t)/(9),\text{ where t is number of years.}`

Hence, the mathematical expression is,

`100*2^{(t)/(9)}`