Question

Scientists have found that the relationship between the area of an island and the number of species can be modeled approximately by S=-3.404+103.2ln(A) S=−3.404+103.2ln(A), where AA is the area in km^2km 2 and SS is the number of species.

Answer 1

`A=e^{(S+3.404/103.2)`

Explanation:

Step one:

we are told that the relationship between the number of species and the island area is given as

`S=-3.404+103.2ln(A)`-----------------1

based on any given value for either area or number of species, we can find the other.

say we want to find the land area for a given amount of specie

Step two:

we first make area A subject of the formula.

`S=-3.404+103.2ln(A)`

let us isolate
`ln(A)`

`S + 3.404 = 103.2ln(A)`

Divide both sides by 103.2 we have

`(S + 3.404)/103.2 = ln(A)`

Now, exponentiate both sides using the base e.

`A=e^{(S+3.404/103.2)`----------------2

for a given value of "S" we can find the area A based on the above expression.