{"id":"cb_question_bank:fd3f6c21-04e6-4127-b131-385cb005d123","source_id":"cb_question_bank","source_item_id":"fd3f6c21-04e6-4127-b131-385cb005d123","external_id":null,"ibn":"032669-DC","question_id":"5c00c2c1","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":"There were no jackrabbits in Australia before 1788 when 24 jackrabbits were introduced. By 1920 the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in the population each year. Which of the following functions best models the population p of t of jackrabbits t years after 1788?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">There were no jackrabbits in Australia before 1788 when 24 jackrabbits were introduced. By 1920 the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in the population each year. Which of the following functions best models the population <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a252d37ee3bca6f66c880f56461c18856e9b55dfecf0f4fe7115cd2efd70971c\" alt=\"p of t\"></span></span> of jackrabbits <span class=\"italic\">t</span> years after 1788?</p>\n","rationale_html":"<p>Choice C is correct. This exponential growth model can be written in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b78825423cf713bf6c05799a9f0e9ca16b7a03e3a7f5f7d9914dead4485d5b62\" alt=\"p of t equals, A, times, open parenthesis, 1 plus r, close parenthesis, raised to the t power\"></span>, where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a252d37ee3bca6f66c880f56461c18856e9b55dfecf0f4fe7115cd2efd70971c\" alt=\"p of t \"></span> is the population <span class=\"italic\">t</span> years after 1788, <span class=\"italic\">A</span> is the initial population, and <span class=\"italic\">r</span> is the yearly growth rate, expressed as a decimal. Since there were 24 jackrabbits in Australia in 1788, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/89a9fde222010a2be7fe315aab0e0b76ef83787834e0a0b860fcb927150118c4\" alt=\"A, equals 24\"></span>. Since the number of jackrabbits increased by an average of 16.2% each year, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e071454dfcdd0049e39c0bfcd9b15f934c25ef11c0148a00f6396d8c45a6a8f1\" alt=\"r equals 0 point 1 6 2\"></span>. Therefore, the equation that best models this situation is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7494e34fcf845802727e0306be334eb0e2c89f95bb3a9e961cb4cc6fca55564d\" alt=\"p of t equals, 24 times, 1 point 1 6 2 raised to the t power\"></span>.</p><p>Choices A, B, and D are incorrect and may result from misinterpreting the form of an exponential growth model.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4d7de3edb285e31f84e03ac84bc2345f88b3baffcce025cba0b21f0a3019634f\" alt=\"p of t equals, 1 point 1 6 2 times, 24 raised to the t power\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0b48aed8c47553c21352d456c6ffb91028734beacf850be1bf896eeae67440c3\" alt=\"p of t equals, 24 times, 2 raised to the 1 point 1 6 2, t power\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aacdd6715db5e6c6a3a9fff8a2593b2974322fddb9118e847b72bf40bc193db6\" alt=\"p of t equals, 24 times, 1 point 1 6 2 raised to the t power\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3d9a2de345064e0393fa5409622e232586bf4b0b9a8b69d3e8c723532c55f43f\" alt=\"p of t equals, open parenthesis, 24 times 1 point 1 6 2, close parenthesis, raised to the t power\"></span></span>\n          </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}}