{"id":248670,"date":"2025-07-08T14:56:11","date_gmt":"2025-07-08T14:56:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248670"},"modified":"2025-07-08T14:56:14","modified_gmt":"2025-07-08T14:56:14","slug":"the-atmospheric-pressure-p-in-pounds-per-square-inch-at-an-altitude-of-h-feet-above-the-earth-is-given-by-the-equation-p-14-7e%e2%88%920-00005h","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/the-atmospheric-pressure-p-in-pounds-per-square-inch-at-an-altitude-of-h-feet-above-the-earth-is-given-by-the-equation-p-14-7e%e2%88%920-00005h\/","title":{"rendered":"The atmospheric pressure P in pounds per square inch at an altitude of h feet above the Earth is given by the equation P = 14.7e\u22120.00005h"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The atmospheric pressure P in pounds per square inch at an altitude of h feet above the Earth is given by the equation P = 14.7e\u22120.00005h. Find the pressure at each altitude. (Round your answers to two decimal places.) (a) 0 ft lb\/in2 (b) 4000 ft lb\/in2 (c) 10,000 ft lb\/in2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve for the atmospheric pressure at various altitudes, we will use the given formula: P=14.7e\u22120.00005hP = 14.7e^{-0.00005h}P=14.7e\u22120.00005h<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PPP is the atmospheric pressure in pounds per square inch (lb\/in\u00b2),<\/li>\n\n\n\n<li>hhh is the altitude in feet,<\/li>\n\n\n\n<li>eee is the base of the natural logarithm (approximately 2.71828).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Calculation:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">(a) Pressure at 0 feet:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">When the altitude is 0 feet (sea level), we can substitute h=0h = 0h=0 into the equation: P=14.7e\u22120.00005(0)=14.7e0=14.7\u2009lb\/in2P = 14.7e^{-0.00005(0)} = 14.7e^0 = 14.7 \\, \\text{lb\/in}^2P=14.7e\u22120.00005(0)=14.7e0=14.7lb\/in2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the pressure at 0 feet is <strong>14.7 lb\/in\u00b2<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">(b) Pressure at 4000 feet:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Now, let\u2019s substitute h=4000h = 4000h=4000 feet into the equation: P=14.7e\u22120.00005(4000)=14.7e\u22120.2P = 14.7e^{-0.00005(4000)} = 14.7e^{-0.2}P=14.7e\u22120.00005(4000)=14.7e\u22120.2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using e\u22120.2\u22480.8187e^{-0.2} \\approx 0.8187e\u22120.2\u22480.8187, we get: P=14.7\u00d70.8187\u224812.04\u2009lb\/in2P = 14.7 \\times 0.8187 \\approx 12.04 \\, \\text{lb\/in}^2P=14.7\u00d70.8187\u224812.04lb\/in2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the pressure at 4000 feet is <strong>12.04 lb\/in\u00b2<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">(c) Pressure at 10,000 feet:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, for h=10,000h = 10,000h=10,000 feet, we substitute into the equation: P=14.7e\u22120.00005(10000)=14.7e\u22120.5P = 14.7e^{-0.00005(10000)} = 14.7e^{-0.5}P=14.7e\u22120.00005(10000)=14.7e\u22120.5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using e\u22120.5\u22480.6065e^{-0.5} \\approx 0.6065e\u22120.5\u22480.6065, we get: P=14.7\u00d70.6065\u22488.91\u2009lb\/in2P = 14.7 \\times 0.6065 \\approx 8.91 \\, \\text{lb\/in}^2P=14.7\u00d70.6065\u22488.91lb\/in2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the pressure at 10,000 feet is <strong>8.91 lb\/in\u00b2<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a) Pressure at 0 ft<\/strong>: 14.7 lb\/in\u00b2<\/li>\n\n\n\n<li><strong>(b) Pressure at 4000 ft<\/strong>: 12.04 lb\/in\u00b2<\/li>\n\n\n\n<li><strong>(c) Pressure at 10,000 ft<\/strong>: 8.91 lb\/in\u00b2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The equation shows that as altitude increases, the atmospheric pressure decreases exponentially due to the e\u22120.00005he^{-0.00005h}e\u22120.00005h term. This is consistent with the fact that the higher you go, the less air there is above you, which leads to lower pressure.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-289.jpeg\" alt=\"\" class=\"wp-image-248671\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The atmospheric pressure P in pounds per square inch at an altitude of h feet above the Earth is given by the equation P = 14.7e\u22120.00005h. Find the pressure at each altitude. (Round your answers to two decimal places.) (a) 0 ft lb\/in2 (b) 4000 ft lb\/in2 (c) 10,000 ft lb\/in2 The Correct Answer and [&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-248670","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248670","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=248670"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248670\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}