Putting It Together: Growth Models

At the beginning of the module, you were introduced to some social media statistics for several celebrities.  Since 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.

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

Photo shows a model posing in front of photographer.

 

Because you know that the number of followers is growing at 5%, you know you’re dealing with exponential growth.  In 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].

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

 

Unfortunately, you won’t quite meet your goal, but you’ll be close.