Geoff planted dahlias in his garden Dahlias have bulbs that divide and reproduce underground in the first year Geoff garden produced 4 bulbs in the second year it produced 8 bulbs and in the third year it produced 16 bulbs if this pattern continues how many bulbs should geoff expect in the tenth year
1. 2,048 blubs
2. 1,024 blubs
3. 40 blubs
4. 32 blubs
3 answers
1. 2,048 bulbs
explain why
The pattern observed in the number of bulbs produced each year is that the number of bulbs doubles every year. This is because dahlias reproduce through bulb division, which essentially produces two new bulbs for every one that already exists. So, in the first year, 1 bulb becomes 2 bulbs; in the second year, 2 bulbs become 4 bulbs; in the third year, 4 bulbs become 8 bulbs, and so on.
Therefore, to calculate the number of bulbs produced in the tenth year, we can simply continue this pattern and double the number of bulbs in the ninth year (which we can calculate by doubling the number of bulbs produced in the eighth year, and so on). Doing this multiplication continuously, we get:
Year 4: 16 bulbs
Year 5: 32 bulbs
Year 6: 64 bulbs
Year 7: 128 bulbs
Year 8: 256 bulbs
Year 9: 512 bulbs
Year 10: 1,024 bulbs
Therefore, option 1, 2,048 bulbs, is incorrect; option 2, 1,024 bulbs, is the correct answer.
Therefore, to calculate the number of bulbs produced in the tenth year, we can simply continue this pattern and double the number of bulbs in the ninth year (which we can calculate by doubling the number of bulbs produced in the eighth year, and so on). Doing this multiplication continuously, we get:
Year 4: 16 bulbs
Year 5: 32 bulbs
Year 6: 64 bulbs
Year 7: 128 bulbs
Year 8: 256 bulbs
Year 9: 512 bulbs
Year 10: 1,024 bulbs
Therefore, option 1, 2,048 bulbs, is incorrect; option 2, 1,024 bulbs, is the correct answer.