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
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.
To solve this problem, we can observe that the number of bulbs doubles each year.
In the first year, there were 4 bulbs.
In the second year, there were 8 bulbs (twice the number from the previous year).
In the third year, there were 16 bulbs (twice the number from the previous year).
If this pattern continues, in the fourth year, there should be 32 bulbs (twice the number from the third year).
To find out how many bulbs Geoff should expect in the tenth year, we can continue this pattern:
4th year: 32 bulbs
5th year: 64 bulbs
6th year: 128 bulbs
7th year: 256 bulbs
8th year: 512 bulbs
9th year: 1024 bulbs
10th year: 2048 bulbs
Therefore, Geoff should expect 2048 bulbs in the tenth year.
So, the correct answer is 1. 2,048 bulbs.