Friday, July 5, 2019

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 70

Based from some Biologists, the equation logS=logc+klogA (The species-area relationship) is the model of the number of species S in a fixed area A, where c and k are positive constants that depend on the type of species and habitat.

a.) Solve the equation for S


logS=logc+logAkLaw of Logarithm loga(AC)=ClogaAlogS=log(cAk)Law of Logarithm loga(AB)=logaA+logaBS=cAkBecause log is one-to-one



b.) Show that if k=3, then doubling the area increases the number of species eight fold, using part (a).


S=c(2A)3Substitute k=3S=8cA3


It shows that when the area is doubled the number of species increases eight times.

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