Question p-t-18

2.1 Nonlinear Functions - Exponential growth and decay functions
0:00

Pt=1,8001.02t

The function P gives the estimated number of marine mammals in a certain area, where t is the number of years since a study began. What is the best interpretation of P0=1,800 in this context?

A.

The estimated number of marine mammals in the area was 102 when the study began.

B.

The estimated number of marine mammals in the area was 1,800 when the study began.

C.

The estimated number of marine mammals in the area increased by 102 each year during the study.

D.

The estimated number of marine mammals in the area increased by 1,800 each year during the study.

P t = 1,800 1.02 t The function P gives the estimated number of marine mammals

Medium-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 B is correct. The function P gives the estimated number of marine mammals in a certain area, where t is the number of years since a study began. Since the value of P0 is the value of Pt when t = 0 , it follows that P0=1,800 means that the value of Pt is 1,800 when t = 0 . Since t is the number of years since the study began, it follows that t = 0 is 0 years since the study began, or when the study began. Therefore, the best interpretation of P0=1,800 in this context is the estimated number of marine mammals in the area was 1,800 when the study began.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.