{"id":47047,"date":"2024-03-12T22:19:49","date_gmt":"2024-03-12T22:19:49","guid":{"rendered":"https:\/\/www.oracletutoring.ca\/blog\/?p=47047"},"modified":"2024-03-12T22:19:50","modified_gmt":"2024-03-12T22:19:50","slug":"exponents-and-logs-a-decay-equation-from-a-half-life","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/exponents-and-logs-a-decay-equation-from-a-half-life\/","title":{"rendered":"Exponents and logs: a decay equation from a half life."},"content":{"rendered":"\n<h2>Tutoring math, you see exponential growth and decay. The tutor mentions an equation from a half life.<\/h2>\n<p>\nExample: a specimen loses half activity every 45 days. Find a equation for it.<\/p>\n<p>\nAnswer: The equation will be of the form P = P<sub>o<\/sub>e^(kt), t in days, where P<sub>o<\/sub> is the starting amount and P is the amount at time t. At the half life, P=P<sub>o<\/sub>\/2, leaving<\/p>\n<p>1\/2 = e^(45k).<\/p>\n<p>\nTaking ln (natural log) of both sides, we get<\/p>\n<p>\nln(1\/2) = 45k. Then, since ln(1\/2) = -ln2,<\/p>\n<p>\n<p>\n-(ln2)\/45 = k<\/p>\nJack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":"<p>Tutoring math, you see exponential growth and decay. The tutor mentions an equation from a half life. Example: a specimen loses half activity every 45 days. Find a equation for it. Answer: The equation will be of the form P &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/exponents-and-logs-a-decay-equation-from-a-half-life\/\"> <span class=\"screen-reader-text\">Exponents and logs: a decay equation from a half life.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-47047","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47047","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=47047"}],"version-history":[{"count":3,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47047\/revisions"}],"predecessor-version":[{"id":47050,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47047\/revisions\/47050"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=47047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=47047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=47047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}