{"id":16060,"date":"2021-04-01T23:56:57","date_gmt":"2021-04-01T23:56:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/putting-it-together-growth-models\/"},"modified":"2021-07-04T03:24:17","modified_gmt":"2021-07-04T03:24:17","slug":"putting-it-together-growth-models","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/putting-it-together-growth-models\/","title":{"raw":"Putting It Together: Growth Models","rendered":"Putting It Together: Growth Models"},"content":{"raw":"At the beginning of the module, you were introduced to some social media statistics for several celebrities. \u00a0Since then you learned that you could describe and compare growth by understanding a little bit about different types of growth, and using a growth model to make a prediction.\r\n\r\nNow how about you be the one tracking the celebrities? \u00a0Imagine that you started a celebrity blog a few years back. \u00a0You write about hot news in Hollywood, and what your favorite celebs are up to. \u00a0Between 2010 and 2012, your blog followers grew at a rate of 5% to 9,500 people. \u00a0You hope to have 20,000 followers by 2020. \u00a0If this growth rate continues, will you meet your goal?\r\n\r\n\"Photo<\/a>\r\n\r\n \r\n\r\nBecause you know that the number of followers is growing at 5%, you know you\u2019re dealing with exponential growth. \u00a0In order to develop a model, you need an initial value. To determine the initial value, you can use the number of followers in 2012 ([latex]P_0[\/latex] = 9,500), and the rate of growth, which is 5% ([latex]r[\/latex] = 5%), and solve for [latex]P_0[\/latex].\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]P_n=\\left(1+r\\right)^nP_0[\/latex]<\/td>\r\nStart with the explicit form of the exponential growth equation.<\/td>\r\n<\/tr>\r\n
[latex]P_n=\\left(1+0.05\\right)^nP_0[\/latex]<\/td>\r\nSubstitute the growth rate, 5%, written as a decimal for [latex]r[\/latex].<\/td>\r\n<\/tr>\r\n
[latex]P_n=\\left(1+0.05\\right)^n9,500[\/latex]<\/td>\r\nSubstitute the initial value, which is the number of followers in 2012, for [latex]P_0[\/latex].<\/td>\r\n<\/tr>\r\n
[latex]P_8=\\left(1+0.05\\right)^89,500[\/latex]<\/td>\r\nSubstitute the number of years between 2012 and 2020 for [latex]n[\/latex].<\/td>\r\n<\/tr>\r\n
[latex]P_8=\\left(1.05\\right)^89,500\\approx14,000[\/latex]<\/td>\r\nEvaluate.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nUnfortunately, you won\u2019t quite meet your goal, but you\u2019ll be close.","rendered":"

At the beginning of the module, you were introduced to some social media statistics for several celebrities. \u00a0Since then you learned that you could describe and compare growth by understanding a little bit about different types of growth, and using a growth model to make a prediction.<\/p>\n

Now how about you be the one tracking the celebrities? \u00a0Imagine that you started a celebrity blog a few years back. \u00a0You write about hot news in Hollywood, and what your favorite celebs are up to. \u00a0Between 2010 and 2012, your blog followers grew at a rate of 5% to 9,500 people. \u00a0You hope to have 20,000 followers by 2020. \u00a0If this growth rate continues, will you meet your goal?<\/p>\n

\"Photo<\/a><\/p>\n

 <\/p>\n

Because you know that the number of followers is growing at 5%, you know you\u2019re dealing with exponential growth. \u00a0In order to develop a model, you need an initial value. To determine the initial value, you can use the number of followers in 2012 ([latex]P_0[\/latex] = 9,500), and the rate of growth, which is 5% ([latex]r[\/latex] = 5%), and solve for [latex]P_0[\/latex].<\/p>\n

\n\n\n\n\n\n\n\n
[latex]P_n=\\left(1+r\\right)^nP_0[\/latex]<\/td>\nStart with the explicit form of the exponential growth equation.<\/td>\n<\/tr>\n
[latex]P_n=\\left(1+0.05\\right)^nP_0[\/latex]<\/td>\nSubstitute the growth rate, 5%, written as a decimal for [latex]r[\/latex].<\/td>\n<\/tr>\n
[latex]P_n=\\left(1+0.05\\right)^n9,500[\/latex]<\/td>\nSubstitute the initial value, which is the number of followers in 2012, for [latex]P_0[\/latex].<\/td>\n<\/tr>\n
[latex]P_8=\\left(1+0.05\\right)^89,500[\/latex]<\/td>\nSubstitute the number of years between 2012 and 2020 for [latex]n[\/latex].<\/td>\n<\/tr>\n
[latex]P_8=\\left(1.05\\right)^89,500\\approx14,000[\/latex]<\/td>\nEvaluate.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

Unfortunately, you won\u2019t quite meet your goal, but you\u2019ll be close.<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\t
CC licensed content, Original<\/div>