{"id":"cb_question_bank:26d133ec-7355-4e0c-9c92-9d419f96f41a","source_id":"cb_question_bank","source_item_id":"26d133ec-7355-4e0c-9c92-9d419f96f41a","external_id":null,"ibn":"025805-DC","question_id":"926c246b","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation above estimates the global data traffic D , in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?","stimulus":"D equals, 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the t power","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4a467afa0ead6a346a2f23f3212fcf76a3800388c2983690e614c334f06d8e6d\" alt=\"D equals, 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the t power\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The equation above estimates the global data traffic <span class=\"italic\">D</span>, in terabytes, for the year that is <span class=\"italic\">t</span> years after 2010. What is the best interpretation of the number 5,640 in this context?</p>\n","rationale_html":"<p>Choice D is correct. Since <span class=\"italic\">t</span> represents the number of years after 2010, the estimated data traffic, in terabytes, in 2010 can be calculated using the given equation when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03be3f9ca86e73f91aae3da5f4c70ddbd7015f7b2182c3cada4a3b84a54d9546\" alt=\"t equals 0\"></span>. Substituting 0 for <span class=\"italic\">t</span> in the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a558845a7706f5526b0b778138d8073250c7d718d6d30ef692a2425fde956680\" alt=\"D equals, 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the 0 power\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64f091954cf30ca6a6b5c651168deed6421d4c4ef803a5c80ee975c9f6e8ebe6\" alt=\"5,640 times 1, equals 5,640\"></span>. Thus, 5,640 represents the estimated data traffic, in terabytes, in 2010.</p><p>Choice A is incorrect. Since the equation is exponential, the amount of increase of data traffic each year isn’t constant. Choice B is incorrect. According to the equation, the percent increase in data traffic each year is 90%. Choice C is incorrect. The estimated data traffic, in terabytes, for the year that is <span class=\"italic\">t</span> years after 2010 is represented by <span class=\"italic\">D</span>, not the number 5,640.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">The estimated amount of increase of data traffic, in terabytes, each year</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">The estimated percent increase in the data traffic, in terabytes, each year</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">The estimated data traffic, in terabytes, for the year that is&nbsp;<span class=\"italic\">t</span> years after 2010</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">The estimated data traffic, in terabytes, in 2010</p>\n","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}}