Anya wants to get into the habit of reading for at least \(20\) minutes each day. She makes a plan to build up her reading gradually over several days. On Day \(1\), she reads for \(5\) minutes. After Day \(1\), she plans to read according to the following pattern:
On even-numbered days, she reads twice as long as she did the day before.
On odd-numbered days, she reads for \(4\) fewer minutes than she did the day before.
If she follows the pattern, on which day is the first time Anya reads for at least \(20\) minutes? Justify your answer.
One way to solve this problem is to create a table to keep track of how long Anya reads each day.
| Day | Even/Odd | Minutes Reading |
|---|---|---|
| \(1\) | odd | \(5\) |
| \(2\) | even | \(5 \times 2 = 10\) |
| \(3\) | odd | \(10 - 4 = 6\) |
| \(4\) | even | \(6 \times 2 = 12\) |
| \(5\) | odd | \(12 - 4 = 8\) |
| \(6\) | even | \(8 \times 2 = 16\) |
| \(7\) | odd | \(16 - 4 = 12\) |
| \(8\) | even | \(12 \times 2 = 24\) |
If she follows the pattern, Anya reads for at least \(20\) minutes on Day \(8\).