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Advanced Math / Nonlinear functions Difficulty: Easy

$upper P left parenthesis t right parenthesis equals 24.8 left parenthesis 1.036 right parenthesis Superscript t$

The function $P$ gives the predicted population, in millions, of a certain country for the period from $1984$ to $2018$ , where $t$ is the number of years after $1984$ . According to the model, what is the best interpretation of the statement “ $upper P left parenthesis 8 right parenthesis$ is approximately equal to $32.91$ ”?

In $1984$ , the predicted population of this country was approximately $8$ million.

In $1984$ , the predicted population of this country was approximately $32.91$ million.

$8$ years after $1984$ , the predicted population of this country was approximately $32.91$ million.

$32.91$ years after $1984$ , the predicted population of this country was approximately $8$ million.

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Explanation

Choice C is correct. The function $P$ gives the predicted population, in millions, of a certain country for the period from $1984$ to $2018$ , where $t$ is the number of years after $1984$ . Since the value of $upper P left parenthesis 8 right parenthesis$ is the value of $P (t)$ when $t equals 8$ , it follows that " $upper P left parenthesis 8 right parenthesis$ is approximately equal to $32.91$ " means that the value of $P (t)$ is approximately equal to $32.91$ when $t equals 8$ . Therefore, the best interpretation of the statement " $upper P left parenthesis 8 right parenthesis$ is approximately equal to $32.91$ " is that $8$ years after $1984$ , the predicted population of this country was approximately $32.91$ million.

Choice A is incorrect. In $1984$ , the predicted population of this country was $24.8$ million, not approximately $8$ million.

Choice B is incorrect. In $1984$ , the predicted population of this country was $24.8$ million, not approximately $32.91$ million.

Choice D is incorrect. $32.91$ years after $1984$ , the predicted population of this country was $24.8 left parenthesis 1.036 right parenthesis Superscript 32.91$ million, or approximately $79.42$ million, not approximately $8$ million.