{"id":7920,"date":"2019-05-22T16:02:05","date_gmt":"2019-05-22T16:02:05","guid":{"rendered":"http:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/exponential_change\/"},"modified":"2019-05-22T16:02:05","modified_gmt":"2019-05-22T16:02:05","slug":"exponential_change","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/exponential_change\/","title":{"rendered":"Exponential change"},"content":{"rendered":"<p>Continuous change that either accelerates or decelerates so that the pattern of change is curvilinear [J-shaped or S-shaped (sigmoid)]. &nbsp;A snowball rolling downhill changes exponentially with time since when it is twice as big, it gathers snow twice as fast. &nbsp;A prime example of exponential change is contained in the theory of population pressure devised by <a href=\"http:\/\/www.ucmp.berkeley.edu\/history\/malthus.html\" data-editable-link=\"http:\/\/www.ucmp.berkeley.edu\/history\/malthus.html&amp;target=_self\" target=\"_self\" rel=\"noopener noreferrer\">Thomas R. Malthus<\/a> (1766-1834) as shown in the figure below:&nbsp;food production increases as a linear function (or what he called an &#8216;arithmetical ratio&#8217;) over historical time while a population changes exponentially (or what he termed as a &#8216;geometrical ratio&#8217;).&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"..\/wp-content\/uploads\/2019\/05\/image038.jpg\" \/><\/div>\n<\/div>\n<p class=\"\" style=\"text-align: center;\">According to the theory of population pressure, food production demonstrates linear change over historical time in contrast to the size of a population that manifests J-shaped exponential change across the same time scale. This theory was one of the essential building blocks of Darwin\u2019s theory of natural selection (the other being artificial selection).&nbsp;<\/p>\n<p class=\"\" style=\"text-align: left;\">&nbsp;See Differential equation, Exponential, Logistic growth curve, Polynomial, Theory of natural selection, Theory of population pressure &nbsp;&nbsp;<\/p>\n<p><\/p>\n<p><\/p>\n<p><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Continuous change that either accelerates or decelerates so that the pattern of change is curvilinear [J-shaped or S-shaped (sigmoid)]. &nbsp;A snowball rolling downhill changes exponentially with time since when it is twice as big, it gathers snow twice as fast. &nbsp;A prime example of exponential change is contained in the theory of population pressure devised &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/exponential_change\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Exponential change&#8221;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2],"class_list":["post-7920","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-glossary","entry"],"_links":{"self":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts\/7920","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/comments?post=7920"}],"version-history":[{"count":0,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts\/7920\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/media?parent=7920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/categories?post=7920"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/tags?post=7920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}