A rabbit population doubles every month. If the population starts at 32 rabbits at the end of the first month, how many rabbits will there be after eight months?(2 points)
The initial number of rabbits is . The common ratio is . The number of rabbits after eight months is .
The initial number of rabbits is 32.
Since the rabbit population doubles every month, the common ratio is 2.
To find the number of rabbits after eight months, we can use the formula for geometric sequence:
a_n = a_1 * r^(n-1),
where a_n is the number of rabbits after n months, a_1 is the initial number of rabbits, r is the common ratio, and n is the number of months.
Plugging in the given values:
a_n = 32 * 2^(8-1)
a_n = 32 * 2^7
a_n = 32 * 128
a_n = 4096
So, after eight months, there will be 4096 rabbits. Answer: \boxed{4096}.