Mariam's farm has a peculiar bull. One day she gave the bull 2 units of fodder and the bull ate 1 unit. The next day, she gave the bull 3 units of fodder and the bull ate 2 units. The day after, she gave the bull 4 units and the bull ate 3 units. This continued, and on the 99th day she gave the bull 100 units and the bull ate 99 units. Represent these quantities as percentages. This task can be distributed among the class. What do you observe?
Day 1: Bull ate 50% of fodder (1/2). Day 2: Bull ate 66.67% (2/3). Day 3: Bull ate 75% (3/4). Day 99: Bull ate 99% (99/100).
Pattern: The percentage the bull eats increases each day, approaching but never reaching 100%.
Formula: Percentage eaten = (n-1)/n × 100, where n is the units given.
Explanation
The chapter presents this as a class activity to explore percentage patterns. Students observe that as the denominator increases, the percentage approaches 100% but never reaches it. This connects to the concept of limits.
Solution Steps
Day 1: 1/2 = 50%
Day 2: 2/3 = 66.67%
Day 3: 3/4 = 75%
...
Day 99: 99/100 = 99%
Pattern: (n-1)/n approaches 100% as n increases