Friday, May 17, 2019

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 68

Estimate a student's score on a Biology test two years after he got a score of 80 on a test covering the same material, by using Ebbinghaus' Law of Forgetting. Assume that c=0.3 and t is measured in months.

logP=log=P0clog(t+1) Model

Solving for P


logP=logP0log(t+1)2Law of Logarithm loga(AC)=ClogaAlogP=logP0(t+1)2Law of Logarithm loga(AB)=logaAlogaBP=P0(t+1)2Because log is one-to-one



Here P0=80,C=0.3 and t is measured in months

In two years: t=24 months

and


P=80(24+1)0.3P=30.46



The student's expected score on Biology test after 2 years is 30.46.

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