{"id":154190,"date":"2022-03-25T23:15:36","date_gmt":"2022-03-25T17:45:36","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/exponential-functions-definition-formula-and-parameters\/"},"modified":"2022-12-22T21:42:13","modified_gmt":"2022-12-22T16:12:13","slug":"exponential-functions-definition-formula-and-parameters","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/","title":{"rendered":"Exponential Functions \u2013 Definition, Formula and Parameters"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#What_is_Exponential_Function\" title=\"What is Exponential Function?\">What is Exponential Function?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Exponential_Function_Formula\" title=\"Exponential Function Formula\">Exponential Function Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Exponential_Growth\" title=\"Exponential Growth\">Exponential Growth<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Exponential_Decay\" title=\"Exponential Decay\">Exponential Decay<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Overview_of_Exponential_Function\" title=\"Overview of Exponential Function\">Overview of Exponential Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Parameters_of_the_Exponential_Function\" title=\"Parameters of the Exponential Function\">Parameters of the Exponential Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Properties_of_Exponential_Functions\" title=\"Properties of Exponential Functions\">Properties of Exponential Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Examples_of_Exponential_Functions\" title=\"Examples of Exponential Functions-\">Examples of Exponential Functions-<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-functions\/#Questions_to_be_solved\" title=\"Questions to be solved:\">Questions to be solved:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Exponential_Function\"><\/span>What is Exponential Function?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An exponential function is a mathematical function in which the independent variable is in the form of an exponent. The most common form of an exponential function is y = a x<\/p>\n<p>In this equation, a is the base and x is the exponent. The value of y will increase exponentially as the value of x increases.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154189 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/exponential-functions-definition-formula-and-parameters.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/exponential-functions-definition-formula-and-parameters.jpg?v=1648230331 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/exponential-functions-definition-formula-and-parameters-300x212.jpg?v=1648230331 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Exponential_Function_Formula\"><\/span>Exponential Function Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The exponential function formula is a mathematical equation that describes the relationship between two variables, typically the x and y coordinates of points on a graph. The equation is y = ax^b, where a and b are constants. This equation can be used to model population growth, radioactive decay, or any other phenomenon that follows an exponential pattern.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Exponential_Growth\"><\/span>Exponential Growth<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The exponential growth of a population or quantity can be described by a mathematical equation in which the population or quantity is represented by the letter P, and the percentage growth rate is represented by the letter r. The equation is written as P = P 0 ert, where P 0 is the initial population or quantity, r is the percentage growth rate, and t is the number of time periods over which the growth is calculated.<\/p>\n<p>For example, if a population of 100 bacteria doubles every hour, the equation would be P = 100e2t. This equation would predict that the population would reach 10,000 bacteria in 10 hours.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Exponential_Decay\"><\/span>Exponential Decay<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An exponential decay equation is a mathematical equation that describes how a quantity decreases over time. The equation is written in the form<\/p>\n<p>,<\/p>\n<p>where is the quantity at time , is the initial quantity, and is the decay constant.<\/p>\n<p>The decay constant is a measure of how quickly the quantity decreases. It is equal to the inverse of the time constant, which is the amount of time it takes for the quantity to decrease by half.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Overview_of_Exponential_Function\"><\/span>Overview of Exponential Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The exponential function is a mathematical function that describes a relationship between two variables, usually x and y, where the y value is a result of repeated multiplication of x by a fixed number, called the base. The exponential function is written as y = bx, where b is the base and x is the exponent.<\/p>\n<p>The exponential function is used in many real-world applications, such as compound interest, population growth, and radioactive decay. It can also be used to model other mathematical relationships, such as the growth of a bacterial population over time.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parameters_of_the_Exponential_Function\"><\/span>Parameters of the Exponential Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The exponential function is a function that is defined by the equation y = bx, where b is a positive number and x is the input variable. The exponential function is also referred to as the ex function.<\/p>\n<p>The exponential function has the following properties:<\/p>\n<p>1. The exponential function is an increasing function.<\/p>\n<p>2. The exponential function is a monotonic function.<\/p>\n<p>3. The exponential function is a continuous function.<\/p>\n<p>4. The exponential function is a differentiable function.<\/p>\n<p>5. The exponential function is a periodic function.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Exponential_Functions\"><\/span>Properties of Exponential Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. The exponential function is continuous.<\/p>\n<p>2. The exponential function is one-to-one.<\/p>\n<p>3. The exponential function is strictly increasing.<\/p>\n<p>4. The exponential function is asymptotic to the y-axis.<\/p>\n<p>5. The exponential function has a unique inverse function.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Examples_of_Exponential_Functions\"><\/span>Examples of Exponential Functions-<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. y=2x<\/p>\n<p>2. y=3x<\/p>\n<p>3. y=5x<\/p>\n<p>4. y=10x<\/p>\n<p>5. y=100x<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Questions_to_be_solved\"><\/span>Questions to be solved:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. What is the capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r?<\/p>\n<p>2. What is the capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r if the plates are spaced a distance of d\/2 apart?<\/p>\n<p>3. What is the capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r if the plates are spaced a distance of d apart?<\/p>\n<p>1. The capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r is:<\/p>\n<p>C = \u03b50\u03b5rA\/d<\/p>\n<p>2. The capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r if the plates are spaced a distance of d\/2 apart is:<\/p>\n<p>C = \u03b50\u03b5rA\/d<\/p>\n<p>3. The capacitance of a parallel plate capacitor with a dielectric of thickness d and permittivity \u03b5r if the plates are spaced a distance of d apart is:<\/p>\n<p>C = \u03b50\u03b5rA<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Exponential Function? An exponential function is a mathematical function in which the independent variable is in the form [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Exponential Functions \u2013 Definition, Formula and Parameters","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Exponential Functions topic of Maths in details explained by subject experts on infinitylearn.com. 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