Question

The researcher decided that the population growth followed a geometric sequence. He wrote the explicit formula a, = 1000(2)^k to model the growth, and used this formula to predict the populations for years 8, 12, and 40. What would be the population for the 8th, 12th, and 40th year? (Show your work)

Answer 1

The population for the 8th, 12th, and 40th year can be calculated using the explicit formula a, = 1000(2)^k. For the 8th year, the population would be 256,000. For the 12th year, the population would be 4,096,000. And for the 40th year, the population would be 1,099,511,627,776,000.

Step-by-step explanation:

To find the population for the 8th, 12th, and 40th year, we can substitute the corresponding values of k into the explicit formula. The explicit formula given is: an= 1000(2)k.

For the 8th year (k = 8), we have: a8 = 1000(2)8 = 1000(256) = 256,000.

For the 12th year (k = 12), we have: a12 = 1000(2)12 = 1000(4096) = 4,096,000.

For the 40th year (k = 40), we have: a40 = 1000(2)40 = 1000(1,099,511,627,776) = 1,099,511,627,776,000.