{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":47425,"title":"Uranium–Lead Dating","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUsing the input data set of the measured Pb-206/U-238 and Pb-207/U-235 ratios of several samples from the same Zircon specimen, determine the age of the specimen (rounded to 1e6 years) by the intersection of the concordant curve with the linear fit of the data. Use 7.04e8 and 4.47e9 for the half-lives of U-235 and U-238 to Pb-207 and Pb-206.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function age = U_Pb_dating(Pb_U35ratio,Pb_U38ratio)\r\n  age=1e9;\r\nend","test_suite":"%%\r\nPb_U38ratio=[.826,.814,.872,.895,.886];\r\nPb_U35ratio=[57.3,56.6,60.6,61.8,61.4];\r\nage=4.246e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.849,.834,.864,.919,.419];\r\nPb_U35ratio=[46.6,46.2,47.7,50.6,17.6];\r\nage=3.894e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.07608,.07726,.07452,.07781];\r\nPb_U35ratio=[.5957,.6042,.5836,.6093];\r\nage=482e6;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.4126,.5019,.4626,.5098,.4925,.5103,.5399];\r\nPb_U35ratio=[10.724,13.198,12.102,13.385,12.967,13.407,14.230];\r\nage=2.752e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[1.232,.912,.694,.893,.913,.850];\r\nPb_U35ratio=[70.1,49.0,36.3,48.7,50.6,46.8];\r\nage=3.878e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2020-11-11T19:31:29.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-11-07T21:26:08.000Z","updated_at":"2026-01-14T13:56:57.000Z","published_at":"2020-11-07T21:34:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the input data set of the measured Pb-206/U-238 and Pb-207/U-235 ratios of several samples from the same Zircon specimen, determine the age of the specimen (rounded to 1e6 years) by the intersection of the concordant curve with the linear fit of the data. 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Use 7.04e8 and 4.47e9 for the half-lives of U-235 and U-238 to Pb-207 and Pb-206.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function age = U_Pb_dating(Pb_U35ratio,Pb_U38ratio)\r\n  age=1e9;\r\nend","test_suite":"%%\r\nPb_U38ratio=[.826,.814,.872,.895,.886];\r\nPb_U35ratio=[57.3,56.6,60.6,61.8,61.4];\r\nage=4.246e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.849,.834,.864,.919,.419];\r\nPb_U35ratio=[46.6,46.2,47.7,50.6,17.6];\r\nage=3.894e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.07608,.07726,.07452,.07781];\r\nPb_U35ratio=[.5957,.6042,.5836,.6093];\r\nage=482e6;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[.4126,.5019,.4626,.5098,.4925,.5103,.5399];\r\nPb_U35ratio=[10.724,13.198,12.102,13.385,12.967,13.407,14.230];\r\nage=2.752e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));\r\n%%\r\nPb_U38ratio=[1.232,.912,.694,.893,.913,.850];\r\nPb_U35ratio=[70.1,49.0,36.3,48.7,50.6,46.8];\r\nage=3.878e9;\r\nassert(isequal(U_Pb_dating(Pb_U35ratio,Pb_U38ratio),age));","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2020-11-11T19:31:29.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-11-07T21:26:08.000Z","updated_at":"2026-01-14T13:56:57.000Z","published_at":"2020-11-07T21:34:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the input data set of the measured Pb-206/U-238 and Pb-207/U-235 ratios of several samples from the same Zircon specimen, determine the age of the specimen (rounded to 1e6 years) by the intersection of the concordant curve with the linear fit of the data. 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