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Advanced Math / Nonlinear functions Difficulty: Hard

For the function $q$ , the value of $q (x)$ decreases by $45 percent sign$ for every increase in the value of $x$ by $1$ . If $q left parenthesis 0 right parenthesis equals 14$ , which equation defines $q$ ?

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Explanation

Choice C is correct. Since the value of $q (x)$ decreases by a fixed percentage, $45 percent sign$ , for every increase in the value of $x$ by $1$ , the function $q$ is a decreasing exponential function. A decreasing exponential function can be written in the form $q (x) = a {(1 - \frac{p}{100})}^{x}$ , where $a$ is the value of $q left parenthesis 0 right parenthesis$ and the value of $q (x)$ decreases by $p %$ for every increase in the value of $x$ by $1$ . If $q left parenthesis 0 right parenthesis equals 14$ , then $a equals 14$ . Since the value of $q (x)$ decreases by $45 percent sign$ for every increase in the value of $x$ by $1$ , $p equals 45$ . Substituting $14$ for $a$ and $45$ for $p$ in the equation $q (x) = a {(1 - \frac{p}{100})}^{x}$ yields $q (x) = 14 {(1 - \frac{45}{100})}^{x}$ , which is equivalent to $q (x) = 14 {(1 - 0.45)}^{x}$ , or $q left parenthesis x right parenthesis equals 14 left parenthesis 0.55 right parenthesis Superscript x$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. For this function, the value of $q (x)$ increases, rather than decreases, by $45 percent sign$ for every increase in the value of $x$ by $1$ .