Respuesta :
The exponential equation that represents the number of followers y the Miami Marlin’s had x years after they joined the site in 2009 is:
[tex]y = 3205(1.85252343783)^x[/tex]
What is an exponential function?
An exponential function is modeled by:
[tex]A(t) = A(0)(b)^t[/tex]
In which:
- A(0) is the initial value.
- b is the rate of change, as a decimal.
In this problem:
- In 2011, the Miami Marlins had about 11,000 followers on a social media site. Since 2011 is 2 years after 2009, the point is (2, 11000).
- Using the 2016 data, the point is (7, 240000).
Given two points, the rate of change is given by:
[tex]b^{7 - 2} = \frac{240000}{11000}[/tex]
[tex]b^5 = 21.818181[/tex]
[tex]b = \sqrt[5]{21.818181}[/tex]
[tex]b = 1.85252343783[/tex]
Then, the equation is:
[tex]y = a(1.85252343783)^x[/tex]
Point (2, 11000) means that when [tex]x = 2, y = 11000[/tex], hence this is used to find a.
[tex]11000 = a(1.85252343783)^2[/tex]
[tex]a = \frac{11000}{(1.85252343783)^2}[/tex]
[tex]a = 3205[/tex]
Hence, the exponential equation is:
[tex]y = 3205(1.85252343783)^x[/tex]
You can learn more about exponential equations at https://brainly.com/question/18790123
