A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% each month. However, factoring in all causes, 80 fish are lost each month.\
Give a recurrence relation for the population of fish after $n$ months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.
Having a serious issue with recursive algorithms, can anyone please help me answer this?
The starting population is $a_0 = 1000$. Each month we have an increase of $10\%$, and each month can be represented as $a_{n-1}$. We will loose $80$ fish each month. Putting all the information together, the recurrence relation will look like: $$a_n = \lfloor a_{n-1} \cdot 1.1 - 80 \rfloor$$
We put floor on this to round it down to the closest integer.
$$a_5 = 1121$$