{"id":12320,"date":"2024-02-20T18:03:53","date_gmt":"2024-02-20T18:03:53","guid":{"rendered":"https:\/\/www.writemyessays.app\/blog\/questions\/creating-your-own-real-world-scenario-involving-derivatives-of-exponential-functions\/"},"modified":"2024-02-20T18:03:53","modified_gmt":"2024-02-20T18:03:53","slug":"creating-your-own-real-world-scenario-involving-derivatives-of-exponential-functions","status":"publish","type":"questions","link":"https:\/\/www.writemyessays.app\/blog\/questions\/creating-your-own-real-world-scenario-involving-derivatives-of-exponential-functions\/","title":{"rendered":"Creating Your Own Real-World Scenario Involving Derivatives of Exponential Functions"},"content":{"rendered":"

For this Critical Thinking Assignment, you will be creating your own real-world scenario and exploring the meaning of differentiation of exponential functions in that context.<\/p>\n

Part I: Complete the following steps:<\/strong><\/strong><\/h4>\n
    \n
  1. Select a real-world scenario that can be modeled by an exponential function and define the function F(x)<\/em> based on your scenario. (Ex.: Suppose that F(x)<\/em> computes the rabbit population on a game reserve that doubles every 6 months. Suppose there were 120 rabbits initially.)<\/li>\n
  2. Write a mathematical expression for F<\/em>(x<\/em>).<\/li>\n
  3. Find the domain and range of F<\/em>(x<\/em>).<\/li>\n
  4. Find F<\/em>(x<\/em>) and F ‘<\/em>(x<\/em>) at any point.<\/li>\n
  5. Find all x<\/em> values for which F ‘<\/em>(x<\/em>) = 0.<\/li>\n<\/ol>\n

    Part II: Based on your work in Part I, discuss the following:<\/strong><\/strong><\/h4>\n
      \n
    1. Discuss if your function F<\/em>(x<\/em>) is differentiable and why. If it is not differentiable, select another function that is and discuss the change you made.<\/li>\n
    2. Discuss the domain and range of F<\/em>(x<\/em>) and why they make sense in the context of your problem.<\/li>\n
    3. Discuss the physical meaning of F<\/em>(x<\/em>) and F ‘<\/em>(x<\/em>) at a point in the context of your problem.<\/li>\n
    4. Discuss what it means for F ‘<\/em>(x<\/em>) = 0 in the context of your problem.<\/li>\n
    5. Reflect on any adjustments you had to make to your original problem context and discuss what characteristics of a real-world context make it a valid choice for applying differentiation concepts to it.<\/li>\n
    6. Provide at least two other real-world situations where differentiation can be applied and respond to the following:\n
        \n
      1. What common characteristics do the real-world scenarios you chose share?<\/li>\n
      2. What did you look for in the way that the real-world scenario can be modeled?<\/li>\n<\/ol>\n<\/li>\n
      3. Discuss the criteria for selecting a real-world scenario that would change if you were seeking to model it with a logarithmic function instead. What key similarities and differences would you find?<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

        For this Critical Thinking Assignment, you will be creating your own real-world scenario and exploring the meaning of differentiation of exponential functions in that context. Part I: Complete the following steps: Select a real-world scenario that can be modeled by an exponential function and define the function F(x) based on your scenario. (Ex.: Suppose that F(x) computes the rabbit […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[122],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/questions\/12320"}],"collection":[{"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/comments?post=12320"}],"version-history":[{"count":0,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/questions\/12320\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/media?parent=12320"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/disciplines?post=12320"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/paper_types?post=12320"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.writemyessays.app\/blog\/wp-json\/wp\/v2\/tagged?post=12320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}