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Advanced Math / Nonlinear functions Difficulty: Easy

The function $f left parenthesis x right parenthesis equals 240,000 left parenthesis 1.22 right parenthesis Superscript x$ gives a company’s predicted annual revenue, in dollars, $x$ years after the company started selling jewelry online, where $0 less than x less than or equals 10$ . What is the best interpretation of the statement “ $f left parenthesis 5 right parenthesis$ is approximately equal to $648,650$ ” in this context?

$5$ years after the company started selling jewelry online, its predicted annual revenue is approximately $648,650$ dollars.

$5$ years after the company started selling jewelry online, its predicted annual revenue will have increased by a total of approximately $648,650$ dollars.

When the company’s predicted annual revenue is approximately $648,650$ dollars, it is $5$ times the predicted annual revenue for the previous year.

When the company’s predicted annual revenue is approximately $648,650$ dollars, it is $5 percent sign$ greater than the predicted annual revenue for the previous year.

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Explanation

Choice A is correct. It’s given that the function $f$ gives a company’s predicted annual revenue, in dollars, $x$ years after the company started selling jewelry online. 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 $648,650$ ” means that $f (x)$ is approximately equal to $648,650$ when $x equals 5$ . Therefore, the best interpretation of the given statement is that $5$ years after the company started selling jewelry online, its predicted annual revenue is approximately $648,650$ dollars.

Choice B is incorrect. The function $f$ gives the predicted annual revenue, not the predicted increase in annual revenue.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect. In the given function, $x$ represents the number of years after the company started selling jewelry online, not the percent increase in revenue from the previous year.