{"id":"cb_question_bank:8e0165a7-0170-4ffb-a57a-62ae32fa4d46","source_id":"cb_question_bank","source_item_id":"8e0165a7-0170-4ffb-a57a-62ae32fa4d46","external_id":"1f9e0de2-d5a7-4f67-9e59-62315da247f3","ibn":null,"question_id":"3122fc7b","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A linear model estimates the population of a city from 1991 to 2015 . The model estimates the population was 57 thousand in 1991 , 224 thousand in 2011 , and x thousand in 2015 . To the nearest whole number, what is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p>A linear model estimates the population of a city from <math alttext=\"1991\"><mn>1991</mn>\n</math> to <math alttext=\"2015\"><mn>2015</mn>\n</math>. The model estimates the population was <math alttext=\"57\"><mn>57</mn>\n</math> thousand in <math alttext=\"1991\"><mn>1991</mn>\n</math>, <math alttext=\"224\"><mn>224</mn>\n</math> thousand in <math alttext=\"2011\"><mn>2011</mn>\n</math>, and <math alttext=\"x\"><mi>x</mi>\n</math> thousand in <math alttext=\"2015\"><mn>2015</mn>\n</math>. To the nearest whole number, what is the value of <math alttext=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"257\"><mn>257</mn></math>. It’s given that a linear model estimates the population of a city from <math alttext=\"1991\"><mn>1991</mn></math> to <math alttext=\"2015\"><mn>2015</mn></math>. Since the population can be estimated using a linear model, it follows that there is a constant rate of change for the model. It’s also given that the model estimates the population was <math alttext=\"57\"><mn>57</mn></math> thousand in <math alttext=\"1991\"><mn>1991</mn></math>, <math alttext=\"224\"><mn>224</mn></math> thousand in <math alttext=\"2011\"><mn>2011</mn></math>, and <math alttext=\"x\"><mi>x</mi></math> thousand in <math alttext=\"2015\"><mn>2015</mn></math>. The change in the population between <math alttext=\"2011\"><mn>2011</mn></math> and <math alttext=\"1991\"><mn>1991</mn></math> is <math alttext=\"224 minus 57\"><mn>224</mn><mo>-</mo><mn>57</mn></math>, or <math alttext=\"167\"><mn>167</mn></math>, thousand. The change in the number of years between <math alttext=\"2011\"><mn>2011</mn></math> and <math alttext=\"1991\"><mn>1991</mn></math> is <math alttext=\"2011 minus 1991\"><mn>2011</mn><mo>-</mo><mn>1991</mn></math>, or <math alttext=\"20\"><mn>20</mn></math>, years. Dividing <math alttext=\"167\"><mn>167</mn></math> by <math alttext=\"20\"><mn>20</mn></math> gives <math alttext=\"167 divided by 20\"><mn>167</mn><mo>/</mo><mn>20</mn></math>, or <math alttext=\"8.35\"><mn>8.35</mn></math>, thousand per year. Thus, the change in population per year from <math alttext=\"1991\"><mn>1991</mn></math> to <math alttext=\"2015\"><mn>2015</mn></math> estimated by the model is <math alttext=\"8.35\"><mn>8.35</mn></math> thousand. The change in the number of years between <math alttext=\"2015\"><mn>2015</mn></math> and&nbsp;<math alttext=\"2011\"><mn>2011</mn></math> is&nbsp;<math alttext=\"2015 minus 2011\"><mn>2015</mn><mo>-</mo><mn>2011</mn></math>, or <math alttext=\"4\"><mn>4</mn></math>, years. Multiplying the change in population per year by the change in number of years yields the increase in population from&nbsp;<math alttext=\"2011\"><mn>2011</mn></math> to&nbsp;<math alttext=\"2015\"><mn>2015</mn></math> estimated by the model: <math alttext=\"left parenthesis 8.35 right parenthesis left parenthesis 4 right parenthesis\"><mfenced><mn>8.35</mn></mfenced><mfenced><mn>4</mn></mfenced></math>, or&nbsp;<math alttext=\"33.4\"><mn>33.4</mn></math>, thousand. Adding the change in population from <math alttext=\"2011\"><mn>2011</mn></math> to <math alttext=\"2015\"><mn>2015</mn></math> estimated by the model to the estimated population in <math alttext=\"2011\"><mn>2011</mn></math> yields the estimated population in <math alttext=\"2015\"><mn>2015</mn></math>. Thus, the estimated population in <math alttext=\"2015\"><mn>2015</mn></math> is <math alttext=\"33.4 plus 224\"><mn>33.4</mn><mo>+</mo><mn>224</mn></math>, or&nbsp;<math alttext=\"257.4\"><mn>257.4</mn></math>, thousand. Therefore to the nearest whole number, the value of <math alttext=\"x\"><mi>x</mi></math> is <math alttext=\"257\"><mn>257</mn></math>.</p>","correct_answer":["257"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.810000+00:00","source_updated_at":"2023-08-02T20:25:59.810000+00:00","options":[],"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}}