{"id":195015,"date":"2025-02-25T11:18:34","date_gmt":"2025-02-25T11:18:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195015"},"modified":"2025-02-25T11:18:37","modified_gmt":"2025-02-25T11:18:37","slug":"a-certain-radioactive-substance-decays-exponentially-with-yearly-decay-factor-of-0-93","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/25\/a-certain-radioactive-substance-decays-exponentially-with-yearly-decay-factor-of-0-93\/","title":{"rendered":"A certain radioactive substance decays exponentially with yearly decay factor of 0.93"},"content":{"rendered":"\n<p>A certain radioactive substance decays exponentially with yearly decay factor of 0.93. There are initially 107 grams present.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The decay of a radioactive substance follows the exponential decay formula:<\/p>\n\n\n\n<p>[<br>A(t) = A_0 \\times (decay \\ factor)^t<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A(t) ) is the amount remaining after time ( t ),<\/li>\n\n\n\n<li>( A_0 ) is the initial amount,<\/li>\n\n\n\n<li>( decay \\ factor ) is 0.93,<\/li>\n\n\n\n<li>( t ) is the number of years.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>The equation describing the decay of the given substance is:<\/p>\n\n\n\n<p>[<br>A(t) = 107 \\times (0.93)^t<br>]<\/p>\n\n\n\n<p>This formula allows us to calculate the remaining amount of the substance after any given number of years.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Exponential decay describes the process where a quantity decreases at a rate proportional to its current value. This is commonly observed in radioactive substances, where atoms disintegrate over time, losing mass at a predictable rate.<\/p>\n\n\n\n<p>In this case, the decay factor is <strong>0.93<\/strong>, meaning that every year, <strong>93%<\/strong> of the substance remains, and <strong>7%<\/strong> is lost. This makes it different from linear decay, where a fixed amount disappears each year.<\/p>\n\n\n\n<p>Let&#8217;s break it down:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Initial State:<\/strong> At ( t = 0 ), the substance starts with <strong>107 grams<\/strong>.<\/li>\n\n\n\n<li><strong>After 1 Year:<\/strong> The mass will be <strong>( 107 \\times 0.93 = 99.51 ) grams<\/strong>.<\/li>\n\n\n\n<li><strong>After 2 Years:<\/strong> The mass will be <strong>( 107 \\times 0.93^2 = 92.54 ) grams<\/strong>.<\/li>\n\n\n\n<li><strong>Long-term Behavior:<\/strong> Over many years, the mass will approach zero but never fully disappear.<\/li>\n<\/ol>\n\n\n\n<p>This exponential decay model is widely used in physics, chemistry, and even finance (e.g., depreciation of assets). Understanding how substances decay helps in <strong>nuclear physics, carbon dating, and medical imaging<\/strong>.<\/p>\n\n\n\n<p>Now, I&#8217;ll generate a graph illustrating the decay.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1508-1024x694.png\" alt=\"\" class=\"wp-image-195016\"\/><\/figure>\n\n\n\n<p>Here is the graph illustrating the exponential decay of the radioactive substance over time. The curve shows how the amount decreases gradually, following the equation ( A(t) = 107 \\times (0.93)^t ). Let me know if you need further clarification!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A certain radioactive substance decays exponentially with yearly decay factor of 0.93. There are initially 107 grams present. The Correct Answer and Explanation is : The decay of a radioactive substance follows the exponential decay formula: [A(t) = A_0 \\times (decay \\ factor)^t] where: Correct Answer: The equation describing the decay of the given substance [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-195015","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=195015"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195015\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}