{"id":"cb_question_bank:0e5358eb-5156-4260-9f5a-4da3a2fc2bfd","source_id":"cb_question_bank","source_item_id":"0e5358eb-5156-4260-9f5a-4da3a2fc2bfd","external_id":"217d73a6-2b65-4411-bdbd-71f2d68adf48","ibn":null,"question_id":"a9084ca4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals 9,000 left parenthesis 0.66 right parenthesis Superscript x The given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997 , and 0 less than or equals x less than or equals 5 . If y equals f left parenthesis x right parenthesis is graphed in the xy -plane, which of the following is the best interpretation of the y -intercept of the graph in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"f left parenthesis x right parenthesis equals 9,000 left parenthesis 0.66 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>9,000</mn><msup><mfenced><mn>0.66</mn></mfenced><mi>x</mi></msup></math></p>\n<p style=\"text-align: left;\">The given function <math alttext=\"f\"><mi>f</mi>\n</math> models the number of advertisements a company sent to its clients each year, where <math alttext=\"x\"><mi>x</mi>\n</math> represents the number of years since <math alttext=\"1997\"><mn>1997</mn></math>, and <math alttext=\"0 less than or equals x less than or equals 5\"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>5</mn></math>. If <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is graphed in the <em>xy</em>-plane, which of the following is the best interpretation of the <em>y</em>-intercept of the graph in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. The <em>y</em>-intercept of a graph in the <em>xy</em>-plane is the point where <math alttext=\"x equals 0\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. For the given function <math alttext=\"f\"><mi>f</mi></math>, the<em>&nbsp;y</em>-intercept of the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane can be found by substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation <math alttext=\"y equals 9,000 left parenthesis 0.66 right parenthesis Superscript x\"><mi>y</mi><mo>=</mo><mn>9,000</mn><msup><mfenced><mn>0.66</mn></mfenced><mi>x</mi></msup></math>, which gives <math alttext=\"y equals 9,000 left parenthesis 0.66 right parenthesis Superscript 0\"><mi>y</mi><mo>=</mo><mn>9,000</mn><msup><mfenced><mn>0.66</mn></mfenced><mn>0</mn></msup></math>. This is equivalent to <math alttext=\"y equals 9,000 left parenthesis 1 right parenthesis\"><mi>y</mi><mo>=</mo><mn>9,000</mn><mfenced><mn>1</mn></mfenced></math>, or <math alttext=\"y equals 9,000\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>9,000</mn>\n</mrow>\n</math>. Therefore, the <em>y</em>-intercept of the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is <math alttext=\"left parenthesis 0 comma 9,000 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>9,000</mn></mrow></mfenced></math>. It’s given that the function&nbsp;<math alttext=\"f\"><mi>f</mi></math> models the number of advertisements a company sent to its clients each year. Therefore, <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> represents the estimated number of advertisements the company sent to its clients each year. It's also given that <math alttext=\"x\"><mi>x</mi>\n</math> represents the number of years since <math alttext=\"1997\"><mn>1997</mn></math>. Therefore, <math alttext=\"x equals 0\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> represents <math alttext=\"0\"><mn>0</mn>\n</math> years since <math alttext=\"1997\"><mn>1997</mn></math>, or <math alttext=\"1997\"><mn>1997</mn></math>. Thus, the best interpretation of the <em>y</em>-intercept of the graph of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is that the estimated number of advertisements the company sent to its clients in <math alttext=\"1997\"><mn>1997</mn></math> was <math alttext=\"9,000\"><mn>9,000</mn>\n</math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.826000+00:00","source_updated_at":"2023-08-02T20:25:59.826000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">The minimum estimated number of advertisements the company sent to its clients during the <math alttext=\"5\"><mn>5</mn>\n</math> years was <math alttext=\"1,708\"><mn>1,708</mn>\n</math>.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The minimum estimated number of advertisements the company sent to its clients during the <math alttext=\"5\"><mn>5</mn>\n</math> years was <math alttext=\"9,000\"><mn>9,000</mn>\n</math>.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The estimated number of advertisements the company sent to its clients in <math alttext=\"1997\"><mn>1997</mn></math> was <math alttext=\"1,708\"><mn>1,708</mn>\n</math>.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">The estimated number of advertisements the company sent to its clients in <math alttext=\"1997\"><mn>1997</mn></math> was <math alttext=\"9,000\"><mn>9,000</mn>\n</math>.</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}