A biology class at Central High School predicted that a local population of
animals will double in size every 12 years. The population at the beginning
of 2014 was estimated to be 50 animals. If P represents the population n
years after 2014, then which of the following equations represents the
class's model of the population over time?
Content: Passport to Advanced Math
Objective: You must identify the correct mathematical notation for an expo-
nential relationship that represents a real-world situation.
Explanation: Choice D is correct. You first recognize that a population that
doubles in size over equal time periods is increasing at an exponential rate.
In a doubling scenario, an exponential growth model can be written in the
form y = a where a is the initial population (that is, the population when
n = 0) and b is the number of years it takes for the population to double in
size. In this case, the initial population is 50, the number of animals at the
beginning of 2014. Therefore, a = 50. The text explains that the population
will double in size every 12 years. Therefore, b = 12.