Question

Some biologists model the number of species S in a fixed area A (such as an island) by the species-area relationship

log S = log c + k log A

where c and k are positive constants that depend on the type of species and habitat.


(a) Solve the equation for S.


S =

(b) Using part (a), if k = 2 and the area is doubled, then by what magnitude is the number of species increased?

Answer 1

If a= bc then log a=logb +logc

if z=c^m
log z=mlogc

Answer 2

a) S=cA^k

b) A=2Ao K=2
S=c(2Ao)^2=c*2^2*Ao^2
S=4cAo^2
therefor the # of species increased by 4.