Chapter 11.3, Problem 59PPS

To determine

Find the number of files will be infected in 20 minutes.

Answer to Problem 59PPS

524,288 files will be infected in 20 minutes.

Explanation of Solution

Given:

A virus goes through a computer, infecting the flies. If one file was infected initially and the total number of files infected doubles every minute, how many files will be infected in 20 minutes? Concept Used:

As one file was infected initially, we know that it is $a_1=1$

As the total number of files infected doubles every minute, we have that it is $r=2$

Calculation:

To find how many files will be infected in 20 minutes, we have to calculate $a_{20}$ by using the formula $a_n=a_1·r^{n-1}$

  $a_1=1;r=2;n=20;\text{Find}{a}_{20}$

  $\begin{array}{l}{a}_n=a_1·r^{n-1}\\ $ a_{00}=1\cdot {(2)}^{20-1}=2^{10}=524,288$\end{array}$ Therefore, 524,288 files will be infected in 20 minutes.

Thus, 524,288 files will be infected in 20 minutes.