Question

When a biological researcher arrived on Wombat Island, there were about 1000 wombats on the island. Their population grew quickly. Estimated Wombat Population Year 1 2 3 4 5 Wombats 1000 2000 4000 8000 16,000 The researcher decided that the population growth followed a geometric sequence. He wrote the explicit formula an = 1000(2)n – 1 to model the growth, and used this formula to predict the populations for years 6, 10, and 50.

Answer 1

Answer:

Yes

Step-by-step explanation: The explicit formula used: An = 1000(2)n - 1 is the correct formula. This is modeled as exponential growth with a common ratio of 2; which is correct based on the data given in the table.

Answer 2

Answer:

. In theory, the researcher's method for predicting the populations is perfect, but there is a flaw to it. That flaw is that at some point, the wombat population will not be able to expand anymore. By his calculations, by year 10, there would be 512,000 wombats on the island. This is likely not possible in practice. It would work for a few years, though.

Step-by-step explanation: