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Advanced Math / Nonlinear functions Difficulty: Easy

$upper P left parenthesis t right parenthesis equals 1,800 left parenthesis 1.02 right parenthesis Superscript t$

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 $upper P left parenthesis 0 right parenthesis equals 1,800$ in this context?

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

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

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

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

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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 $upper P left parenthesis 0 right parenthesis$ is the value of $P (t)$ when $t equals 0$ , it follows that $upper P left parenthesis 0 right parenthesis equals 1,800$ means that the value of $P (t)$ is $1,800$ when $t equals 0$ . Since $t$ is the number of years since the study began, it follows that $t equals 0$ is $0$ years since the study began, or when the study began. Therefore, the best interpretation of $upper P left parenthesis 0 right parenthesis equals 1,800$ 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.