Geoff planted dahlias in his garden. Dahlias have bullbs that dvide and reproduce underground. in the first year, geoff's 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?
apparently, in the nth year, it produces 2*2^n bulbs, so ...
Bulbs = 2^(n+1). n = The number of years.
In the 10th year: Bulbs = 2^(10+1) = 2^11.
bulbs = 2^n+1)
To find out how many bulbs Geoff should expect in the tenth year, let's analyze the pattern. We can observe that the number of bulbs doubles each year.
In the first year, Geoff had 4 bulbs.
In the second year, the 4 bulbs divided and doubled to become 8 bulbs.
In the third year, the 8 bulbs again divided and doubled to become 16 bulbs.
So, we can say that each year the number of bulbs doubles. To find out how many bulbs Geoff should expect in the tenth year, we need to continue doubling the number of bulbs.
Starting with 16 bulbs in the third year, we can calculate as follows:
Year 4: 16 * 2 = 32 bulbs
Year 5: 32 * 2 = 64 bulbs
Year 6: 64 * 2 = 128 bulbs
Year 7: 128 * 2 = 256 bulbs
Year 8: 256 * 2 = 512 bulbs
Year 9: 512 * 2 = 1024 bulbs
Year 10: 1024 * 2 = 2048 bulbs
Therefore, Geoff should expect 2048 bulbs in the tenth year.