Question f-x-30

2.1 Nonlinear Functions - Exponential growth and decay functions
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fx=3,0000.75x

A conservation scientist implemented a program to reduce the population of a certain species in an area. The given function estimates this species' population x years after 2008, where x8. Which of the following is the best interpretation of 3,000 in this context?

A.

The estimated percent decrease in the population for this species and area every 8 years after 2008

B.

The estimated percent decrease in the population for this species and area each year after 2008

C.

The estimated population for this species and area 8 years after 2008

D.

The estimated initial population for this species and area in 2008

f x = 3,000 0.75 x A conservation scientist implemented a program to reduce the population

Hard-difficulty · SAT Math · Nonlinear Functions — Exponential growth and decay functions. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. Substituting 0 for x in the given equation yields f0=3,0000.750, which is equivalent to f0=3,0001, or f0=3,000. It’s given that the function estimates the species’ population x years after 2008, so it follows that the estimated population of the species is 3,000 in 2008. Therefore, the best interpretation of 3,000 in this context is the estimated initial population for this species and area in 2008.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect. The estimated percent decrease in the population for this species and area each year after 2008 is 25%, not 3,000 .

Choice C is incorrect. The estimated population for this species and area 8 years after 2008 is 3,0000.758, or approximately 300 , not 3,000 .