Geoff planted dahlias in his garden. dahlias have bulbs that divide and reproduce underground. in the first year, Geoff's garden produced 6 bulbs. in the second years, it produced 12 bulbs, and in the third year, it produced 24 bulbs. if this pattern continues, how many bulbs should geoff expect in the eighth year?
48 bulbs
384 bulbs
768 bulbs
1,536 bulbs
768
To find the pattern in the number of bulbs produced each year, we can observe that the number of bulbs is doubling each year.
In the first year, there were 6 bulbs.
In the second year, there were 2 times the number of bulbs in the first year, which is 2 * 6 = 12 bulbs.
In the third year, there were 2 times the number of bulbs in the second year, which is 2 * 12 = 24 bulbs.
Therefore, in each subsequent year, the number of bulbs is doubling. So, in the fourth year, there would be 2 times the number of bulbs in the third year, which is 2 * 24 = 48 bulbs.
Following the same pattern, in the eighth year, there would be 2 times the number of bulbs in the seventh year, which is 2 * 192 = 384 bulbs.
Therefore, Geoff should expect 384 bulbs in the eighth year. So the correct answer is 384 bulbs.
To find out how many bulbs Geoff should expect in the eighth year, we need to identify the pattern in the number of bulbs produced each year.
From the given information, we can see that the number of bulbs doubles each year. In the first year, there were 6 bulbs, in the second year, there were 12 bulbs, and in the third year, there were 24 bulbs.
To find out how many bulbs Geoff should expect in the eighth year, we can continue this pattern:
- In the fourth year, there would be 24 x 2 (48) bulbs.
- In the fifth year, there would be 48 x 2 (96) bulbs.
- In the sixth year, there would be 96 x 2 (192) bulbs.
- In the seventh year, there would be 192 x 2 (384) bulbs.
- And finally, in the eighth year, there would be 384 x 2 (768) bulbs.
Therefore, Geoff should expect 768 bulbs in the eighth year. So the correct answer is 768 bulbs.