{"id":1987,"date":"2016-11-02T23:09:44","date_gmt":"2016-11-02T23:09:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=1987"},"modified":"2017-04-04T19:30:46","modified_gmt":"2017-04-04T19:30:46","slug":"why-it-matters-exponential-and-logarithmic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/why-it-matters-exponential-and-logarithmic-functions\/","title":{"raw":"Why It Matters: Exponential and Logarithmic Functions","rendered":"Why It Matters: Exponential and Logarithmic Functions"},"content":{"raw":"<h2>Why learn about exponential and logarithmic functions?<\/h2>\r\nMany sources credit Albert Einstein as saying, \u201cCompound interest is the eighth wonder of the world. \u00a0He who understands it, earns it ... he who doesn't ... pays it.\u201d \u00a0You probably already know this if you have ever invested in an account or taken out a loan. \u00a0Interest is the amount added to the balance. \u00a0The beauty, in the case of investing, is that once interest is earned, it also earns interest. \u00a0This idea of interest earning interest is known as compound interest. \u00a0(It isn\u2019t quite as beautiful on money you owe.)\r\n\r\nInterest can be compounded over different time intervals. \u00a0It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). \u00a0And then there is one more option\u2014continuous compounding\u2014which is the theoretical concept of adding interest in infinitesimally small increments. \u00a0Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.\r\n\r\n<img class=\"wp-image-3911 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27155146\/17299241862_6f406bfbca_o-300x184.jpg\" alt=\"\" width=\"450\" height=\"276\" \/>\r\n\r\n&nbsp;\r\n\r\nSuppose you inherit $10,000. \u00a0You decide to invest in in an account paying 3% interest compounded continuously. \u00a0How can you calculate the balance be in 5 years, 10 years, and 50 years? \u00a0You\u2019ll want to know, especially for retirement planning.\r\n\r\nIn this module, you will learn about the function you can evaluate to answer these questions. \u00a0And you will discover how to make changes to the variables involved, such as time or initial investment, to alter your results.\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nExponential Functions\r\n<ul>\r\n \t<li>Evaluate an exponential growth function with different bases<\/li>\r\n \t<li>Use a compound interest formula<\/li>\r\n \t<li>Write an exponential function<\/li>\r\n \t<li>Find an exponential function given a graph<\/li>\r\n \t<li>Use a graphing calculator to find an exponential function<\/li>\r\n \t<li>Find an exponential function that models continuous growth or decay<\/li>\r\n<\/ul>\r\nGraphs of Exponential Functions\r\n<ul>\r\n \t<li>Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\r\n \t<li>Graph exponential functions using transformations.<\/li>\r\n<\/ul>\r\nLogarithmic Functions\r\n<ul>\r\n \t<li>Convert from logarithmic to exponential form.<\/li>\r\n \t<li>Convert from exponential to logarithmic form.<\/li>\r\n \t<li>Evaluate common and natural logarithms.<\/li>\r\n<\/ul>\r\nGraphs of Logarithmic Functions\r\n<ul>\r\n \t<li>Identify the domain of a logarithmic function.<\/li>\r\n \t<li>Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\r\n \t<li>Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;","rendered":"<h2>Why learn about exponential and logarithmic functions?<\/h2>\n<p>Many sources credit Albert Einstein as saying, \u201cCompound interest is the eighth wonder of the world. \u00a0He who understands it, earns it &#8230; he who doesn&#8217;t &#8230; pays it.\u201d \u00a0You probably already know this if you have ever invested in an account or taken out a loan. \u00a0Interest is the amount added to the balance. \u00a0The beauty, in the case of investing, is that once interest is earned, it also earns interest. \u00a0This idea of interest earning interest is known as compound interest. \u00a0(It isn\u2019t quite as beautiful on money you owe.)<\/p>\n<p>Interest can be compounded over different time intervals. \u00a0It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). \u00a0And then there is one more option\u2014continuous compounding\u2014which is the theoretical concept of adding interest in infinitesimally small increments. \u00a0Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3911 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/27155146\/17299241862_6f406bfbca_o-300x184.jpg\" alt=\"\" width=\"450\" height=\"276\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Suppose you inherit $10,000. \u00a0You decide to invest in in an account paying 3% interest compounded continuously. \u00a0How can you calculate the balance be in 5 years, 10 years, and 50 years? \u00a0You\u2019ll want to know, especially for retirement planning.<\/p>\n<p>In this module, you will learn about the function you can evaluate to answer these questions. \u00a0And you will discover how to make changes to the variables involved, such as time or initial investment, to alter your results.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Exponential Functions<\/p>\n<ul>\n<li>Evaluate an exponential growth function with different bases<\/li>\n<li>Use a compound interest formula<\/li>\n<li>Write an exponential function<\/li>\n<li>Find an exponential function given a graph<\/li>\n<li>Use a graphing calculator to find an exponential function<\/li>\n<li>Find an exponential function that models continuous growth or decay<\/li>\n<\/ul>\n<p>Graphs of Exponential Functions<\/p>\n<ul>\n<li>Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\n<li>Graph exponential functions using transformations.<\/li>\n<\/ul>\n<p>Logarithmic Functions<\/p>\n<ul>\n<li>Convert from logarithmic to exponential form.<\/li>\n<li>Convert from exponential to logarithmic form.<\/li>\n<li>Evaluate common and natural logarithms.<\/li>\n<\/ul>\n<p>Graphs of Logarithmic Functions<\/p>\n<ul>\n<li>Identify the domain of a logarithmic function.<\/li>\n<li>Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\n<li>Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1987\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Why It Matters: Exponential and Logarithmic Functions. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Piggy bank on dollar bills. <strong>Authored by<\/strong>: Pictures of Money. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.flickr.com\/photos\/pictures-of-money\/17299241862\/\">https:\/\/www.flickr.com\/photos\/pictures-of-money\/17299241862\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Why It Matters: Exponential and Logarithmic Functions\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Piggy bank on dollar bills\",\"author\":\"Pictures of Money\",\"organization\":\"\",\"url\":\"https:\/\/www.flickr.com\/photos\/pictures-of-money\/17299241862\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"bd5a2f06-ca37-4209-a444-8d78e4dc01fb","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1987","chapter","type-chapter","status-publish","hentry"],"part":1964,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1987","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1987\/revisions"}],"predecessor-version":[{"id":3917,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1987\/revisions\/3917"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1964"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1987\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=1987"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1987"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1987"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=1987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}