# Future of libraries

You know that thanks to the Internet, electronic communications and developing online resources on the Internet annually declining number of traditional readership by 17%. These deal is irreversible evolutionary shift from old books from libraries to immediately available and cheaper information from the Internet.

The library had in 1991 3336 readers. Determine the year in which count of readers will be only 289.

Correct result:

x =  2004

#### Solution:

$p=1-17/100=\dfrac{ 83 }{ 100 }=0.83 \ \\ \ \\ 3336 \cdot \ p^{ x-1991 }=289 \ \\ (x-1991) \ln=\ln 289 - \ln 3336 \ \\ x=1991 + (\ln (289) -\ln (3336))/ \ln (p)=1991 + (\ln 289 -\ln 3336)/ \ln 0.83=2004$

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