Question

SOCIAL MEDIA In 2011, the Miami Marlins had about 11,000 followers on a social media site. In 2016, they had about 240,000 followers. Which equation represents the number of followers y the Miami Marlin’s had x years after they joined the site in 2009?

Answer 1

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:

$y = 3205(1.85252343783)^x$

What is an exponential function?

An exponential function is modeled by:

$A(t) = A(0)(b)^t$

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:

$b^{7 - 2} = \frac{240000}{11000}$

$b^5 = 21.818181$

$b = \sqrt[5]{21.818181}$

$b = 1.85252343783$

Then, the equation is:

$y = a(1.85252343783)^x$

Point (2, 11000) means that when $x = 2, y = 11000$, hence this is used to find a.

$11000 = a(1.85252343783)^2$

$a = \frac{11000}{(1.85252343783)^2}$

$a = 3205$

Hence, the exponential equation is:

$y = 3205(1.85252343783)^x$

You can learn more about exponential equations at brainly.com/question/18790123