precal
posted by melek .
Some biologists model the number of species S in a fixed area A (such as an island) by the speciesarea 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?

If a= bc then log a=logb +logc
if z=c^m
log z=mlogc 
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.