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.

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samuelonum1 samuelonum1 · Answer 1 · 2020-11-15T09:45:45+01:00

Answer:

[tex]A=e^{(S+3.404/103.2)[/tex]

Step-by-step explanation:

Step one:

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

[tex]S=-3.404+103.2ln(A)[/tex]-----------------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.

[tex]S=-3.404+103.2ln(A)[/tex]

let us isolate [tex]ln(A)[/tex]

[tex]S + 3.404 = 103.2ln(A)[/tex]

Divide both sides by 103.2 we have

[tex](S + 3.404)/103.2 = ln(A)[/tex]

Now, exponentiate both sides using the base e.

[tex]A=e^{(S+3.404/103.2)[/tex]----------------2

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