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Advanced Math / Nonlinear functions Difficulty: Medium

The equation $upper E left parenthesis t right parenthesis equals 5 left parenthesis 1.8 right parenthesis Superscript t$ gives the estimated number of employees at a restaurant, where $t$ is the number of years since the restaurant opened. Which of the following is the best interpretation of the number $5$ in this context?

The estimated number of employees when the restaurant opened

The increase in the estimated number of employees each year

The number of years the restaurant has been open

The percent increase in the estimated number of employees each year

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Explanation

Choice A is correct. For an exponential function of the form $E (t) = a {(b)}^{t}$ , where $a$ and $b$ are constants, the initial value of the function—that is, the value of the function when $t equals 0$ —is $a$ and the value of the function increases by a factor of $b$ each time $t$ increases by $1$ . Since the function $upper E left parenthesis t right parenthesis equals 5 left parenthesis 1.8 right parenthesis Superscript t$ gives the estimated number of employees at a restaurant and $t$ is the number of years since the restaurant opened, the best interpretation of the number $5$ in this context is the estimated number of employees when $t equals 0$ , or when the restaurant opened.

Choice B 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.