Since the area of a square is equal to the square of one of its side's length, then the area should be equivalent to . ---> equation (1) By using pythagoras rule which states that the ---> equation (2) where the opposite side's length is 8 and the hypotenuse side's length is 10 by substituting by the values in equation (2) therefore, substitute this value in equation (1) then where A is the area of the square whose side is x
Taking into account that the growth rate of the number of species on the island is proportional to the density of species (number of species between area of the island), a model based on a differential equation is proposed:
This differential equation can be solved by the method of separable variables like this:
with what you get:
. Taking exponentials on both sides of the equation: