Question

A new DVD is available for sale in a store one week after
its release. The cumulative revenue, $R, from sales of the
DVD in this store in week t after its release is R=f(t)=360lnt with t>1. Find f'(2) and the relative rate of change ((f'))/(f) at t = 2.

Answer 1

I read this as R=f(t)=360ln(t) for t>1. f(2)=360ln(2)=$249.53.

f'(t)=360/t; f'(2)=360/2=$180 per week.

Relative rate of change=f'(2)/f(2)=180/249.53=1/(2ln(2))=0.721 approx.