{"@context":"https://schema.org/","@type":"Quiz","name":"

For the function $q$, the value of $q(x)$ decreases by $45%$ for every increase in the value of $x$ by $1$. If $q(0)=14$, whichequation defines $q$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-203"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

For the function $q$, the value of $q(x)$ decreases by $45%$ for every increase in the value of $x$ by $1$. If $q(0)=14$, whichequation defines $q$?

","comment":{"@type":"Comment","text":"

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

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 $45%$ for every increasein the value of $x$ by $1$.

"},"encodingFormat":"text/markdown","text":"

For the function $q$, the value of $q(x)$ decreases by $45%$ for every increase in the value of $x$ by $1$. If $q(0)=14$, whichequation defines $q$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$q(x)=0.55(14)^{x}$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$q(x)=1.45(14)^{x}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$q(x)=14(1.45)^{x}$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$q(x)=14(0.55)^{x}$

","comment":{"@type":"Comment","text":"

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 $45%$ for every increasein the value of $x$ by $1$.

"},"answerExplanation":{"@type":"Comment","text":"

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 $45%$ for every increasein the value of $x$ by $1$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-203"}