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Advanced Math / Nonlinear functions Difficulty: Medium

The function $f left parenthesis x right parenthesis equals 206 left parenthesis 1.034 right parenthesis Superscript x$ models the value, in dollars, of a certain bank account by the end of each year from $1957$ through $1972$ , where $x$ is the number of years after $1957$ . Which of the following is the best interpretation of “ $f left parenthesis 5 right parenthesis$ is approximately equal to $243$ ” in this context?

The value of the bank account is estimated to be approximately $5$ dollars greater in $1962$ than in $1957$ .

The value of the bank account is estimated to be approximately $243$ dollars in $1962$ .

The value, in dollars, of the bank account is estimated to be approximately $5$ times greater in $1962$ than in $1957$ .

The value of the bank account is estimated to increase by approximately $243$ dollars every $5$ years between $1957$ and $1972$ .

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Explanation

Choice B is correct. It’s given that the function $f left parenthesis x right parenthesis equals 206 left parenthesis 1.034 right parenthesis Superscript x$ models the value, in dollars, of a certain bank account by the end of each year from $19 57$ through $19 72$ , where $x$ is the number of years after $19 57$ . It follows that $f (x)$ represents the estimated value, in dollars, of the bank account $x$ years after $19 57$ . Since the value of $f left parenthesis 5 right parenthesis$ is the value of $f (x)$ when $x equals 5$ , it follows that “ $f left parenthesis 5 right parenthesis$ is approximately equal to $243$ ” means that $f (x)$ is approximately equal to $243$ when $x equals 5$ . In the given context, this means that the value of the bank account is estimated to be approximately $243$ dollars $5$ years after $19 57$ . Therefore, the best interpretation of the statement “ $f left parenthesis 5 right parenthesis$ is approximately equal to $243$ ” in this context is the value of the bank account is estimated to be approximately $243$ dollars in $19 62$ .

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.