pre-cal

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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?

  • pre-cal -

    If a= bc then log a=logb +logc

    if z=c^m
    log z=mlogc

  • pre-cal -

    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.

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