新SAT数学OG样题-Multiple choice题型例题（4）

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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?

新SAT数学OG样题-Multiple choice题型解析汇总，点击查看

Content: Passport to Advanced Math

Key D

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.