Future of libraries

You know that thanks to the Internet, electronic communications, and the development of online resources, the number of traditional readers annually declines by 17%. This is the 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 the count of readers will be only 289.

Correct answer:

x =  2004

Step-by-step explanation:

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

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