Fall 2008 Problem 2: Growing Fern
A fast growing fern starts out with a height of 3 inches. The first day, it grows by two-thirds; the second day, it grows by two-fifths; the third day, it grows by two-sevenths, and so on. On what day will it reach a height of 75 inches?
Solution
Our first correct solution came from Matthew Chumley. He also had the best explanation (see below), earning him 4 points.
If we exam the height of the plant on the first three days, we can come up with the equation (2*d)+3 = h, where d is the day and h is the height of the fern at the end of the day. Here is how we can find it. Day 1 the height is 5, Day 2 the height is 7, and Day 3 the height is 9, so on day n the height would be (2*n)+3. So, if we want to know what day the fern will reach 75 inches, then we must plug in 75 for h in our equation. 75 = (2*d)+3 -> 72 = (2*d) -> 72/2 = d = 36. Therefore, on Day 36, the fern will reach a height of 75 inches.
Other correct solutions (earning two points) came from Brent Krise, Susan Edwards, and Tracy Apgar. Several students (Amanda Cassidy and Jeffery James) were one day off (starting at day one instead of day zero) —- I decided to give two points credit for those solutions. Correct solutions from non-Centenary students came from: Mark Goadrich, Micah Strange, Mary Garrett, Amy Hammond, Jared Latiolais, Derek Smith, and Don Dinnerville.