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A sheet is folded in half a number of times - Junior Cycle Mathematics - Question 4 - 2018
Question 4
A sheet is folded in half a number of times. After 1 fold, there are 2 layers. After 2 folds, there are 4 layers. After 3 folds, there are 8 layers, and so on. (a) ... show full transcript
Worked Solution & Example Answer:A sheet is folded in half a number of times - Junior Cycle Mathematics - Question 4 - 2018
Step 1
Fill in the table to show the number of layers after each of the first 6 folds.
Answer
The number of layers after each fold is as follows:
- After 1 fold: 2 layers
- After 2 folds: 4 layers
- After 3 folds: 8 layers
- After 4 folds: 16 layers
- After 5 folds: 32 layers
- After 6 folds: 64 layers
Thus, the completed table will be:
Number of layers
2 4 8 16 32 64
Step 2
Work out the least number of folds that would be needed to have more than 500 layers.
Answer
To find the least number of folds to exceed 500 layers, we can continue the pattern of doubling layers:
- After 4 folds: 16 layers
- After 5 folds: 32 layers
- After 6 folds: 64 layers
- After 7 folds: 128 layers
- After 8 folds: 256 layers
- After 9 folds: 512 layers
Thus, to have more than 500 layers, at least 9 folds are needed.
Step 3
Put a tick in the correct box to show what kind of pattern is made by the number of layers. Justify your answer.
Answer
Tick: exponential
Justification: The number of layers doubles with each fold, indicating an exponential growth pattern, where the layers can be modeled as , where is the number of layers and is the number of folds.
Step 4
Roughly how many layers will there be after 3 more folds?
Answer
If there are roughly 1 million layers after a certain number of folds, after 3 additional folds, the number of layers can be calculated as follows:
1 million layers roughly doubles with each fold. Therefore, after 3 more folds:
Thus, there will be roughly 8 million layers after 3 more folds.