Geometric Problem

[Professortai]

The area of the flat screen of a computer tablet is 1000 square units. The computer tablet infected with a malware virus has resulted in its flat rectangular screen being affected by 1/3 of the screen being blocked on the first day. On each successive day it blocks a further portion of the screen, as big as a 1/3 of the area it blocked on the previous day.

1. Determine the area that was blocked on the first day.
2. Determine the area of the flat screen that was blocked on the 2nd day.
3. Calculate the maximum area of the flat screen that will eventually be blocked out if the malware acts indefinitely.

 

[Deleted member 4993]

The area of the flat screen of a computer tablet is 1000 square units. The computer tablet infected with a malware virus has resulted in its flat rectangular screen being affected by 1/3 of the screen being blocked on the first day. On each successive day it blocks a further portion of the screen, as big as a 1/3 of the area it blocked on the previous day.

1. Determine the area that was blocked on the first day.
2. Determine the area of the flat screen that was blocked on the 2nd day.
3. Calculate the maximum area of the flat screen that will eventually be blocked out if the malware acts indefinitely.

This is a problem of geometric series. Have you learned to calculate the sum of a geometric series?

Please share your work/thoughts.

 

[HallsofIvy]

The area of the flat screen of a computer tablet is 1000 square units. The computer tablet infected with a malware virus has resulted in its flat rectangular screen being affected by 1/3 of the screen being blocked on the first day. On each successive day it blocks a further portion of the screen, as big as a 1/3 of the area it blocked on the previous day.

1. Determine the area that was blocked on the first day.

1/3 of 1000= ??

2. Determine the area of the flat screen that was blocked on the 2nd day.

(1/3)1000+ (1/3)(1/3)1000= 1000(1/3+ 1/9)

3. Calculate the maximum area of the flat screen that will eventually be blocked out if the malware acts indefinitely.

10000(1/3+ 1/9+ 1/27+ 1/81+ ...)
A geometric sequence, 1+ r+ r^2+ r^3+ .... converges to 1/(1- r). Notice that this does NOT have the initial "1".