Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with

5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.

Write a function, f (x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.

f (x) = 5000·1.12^x

Step-by-step explanation:

A "growth factor" of 12% means the number of bees will decline significantly each month. We assume the problem intends to specify a "growth rate" of 12%, which convert to a growth factor as follows:

growth factor = 1 + growth rate = 1 + 12% = 1.12

Then the exponential equation is ...

population = (initial population) (growth factor) ^x

f (x) = 5000·1.12^x

The answer is f (x) = 5000 (0.12) ^x