Question

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?

Answer 1

Let
x---------------> number of bulbs produced per year
n--------------> number of years
we know that
the pattern can be modeled through the following equation
x=6*[2^(n-1)]

for n=1 year
x=6*[2^(1-1)]----------> 6 bulbs

for n=2 year
x=6*[2^(2-1)]----------> 12 bulbs

for n=3 year
x=6*[2^(3-1)]----------> 24 bulbs

for n=8 year
x=6*[2^(8-1)]----------> 6*128=768 bulbs

the answer is 768 bulbs