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 year, 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?
A. 48 bulbs
B. 384 bulbs
C. 768 bulbs
D. 1,536 bulbs
I'm thinking it's A.
Bulbs = 2^n * 3. n = the number of years.
1st year: 2^1 * 3 = 6 bulbs.
2nd year: 2^2 * 3 = 12 bulbs.
3rd year: 2^3 * 3 = 24 bulbs.
8th year: 2^8 * 3 = 768 bulbs.
every year it multiplies by 2
48 would be the FOURTH year
a = 6
r = 2
https://www.mathsisfun.com/algebra/sequences-sums-geometric.html
To determine the pattern in the number of bulbs produced each year, we observe that the number of bulbs doubles each year.
In the first year, there were 6 bulbs.
In the second year, 6 x 2 = 12 bulbs were produced.
In the third year, 12 x 2 = 24 bulbs were produced.
Based on the pattern, we can calculate the number of bulbs produced in the 8th year by doubling the previous year's number of bulbs:
In the fourth year, 24 x 2 = 48 bulbs were produced.
In the fifth year, 48 x 2 = 96 bulbs were produced.
In the sixth year, 96 x 2 = 192 bulbs were produced.
In the seventh year, 192 x 2 = 384 bulbs were produced.
In the eighth year, 384 x 2 = 768 bulbs.
Therefore, the correct answer is C. Geoff should expect 768 bulbs in the eighth year.
To solve this problem, we need to analyze the pattern in the number of bulbs produced each year.
In the first year, Geoff's garden produced 6 bulbs.
In the second year, it produced 12 bulbs, which is twice the number produced in the first year.
In the third year, it produced 24 bulbs, which is again twice the number produced in the previous year.
We can see that the number of bulbs doubles each year. So, for each subsequent year, we just need to double the number of bulbs produced in the previous year.
Let's continue this pattern:
In the fourth year, we double the number of bulbs produced in the third year, which is 24 * 2 = 48 bulbs.
In the fifth year, we double the number of bulbs produced in the fourth year, which is 48 * 2 = 96 bulbs.
In the sixth year, we double the number of bulbs produced in the fifth year, which is 96 * 2 = 192 bulbs.
In the seventh year, we double the number of bulbs produced in the sixth year, which is 192 * 2 = 384 bulbs.
In the eighth year, we double the number of bulbs produced in the seventh year, which is 384 * 2 = 768 bulbs.
Therefore, the correct answer is C. Geoff should expect 768 bulbs in the eighth year.