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Scenario
Three friends are comparing how fast their social media posts have spread with the goal of having the most shares. Their results are shown below.

Amber: Amber shared her photo with 3 friends. They continue sharing the picture every day, so the number of shares can be represented by f(x) = 34x

Ben: Ben shared his photo with 2 friends. Each of those friends share with 3 more each day, so the number of shares triples every day.
Day
Number of Shares
0
2
1
6
2
18

Carter: Carter shares his post with 10 friends, who each share the post with only 2 friends each day.Exponential Functions
1) Ben’s social media post: ____________________________

2) Carter’s social media post: _____________________________

Sagot :

The function that gives the shares received by a post whereby each friend

shares the post a constant multiple of times each day is exponential.

Responses;

  • Ben's social media post: 2 × 3ⁿ
  • Carter's social media post: 10 × 2ⁿ

Methods by which the above expressions are obtained:

Ben's social media posts;

Given:

The given table of values for Ben's social media post is presented as follows;

[tex]\begin{tabular}{|c|c|}Day&Number of shares\\0&2\\1&6\\2&18\end{array}\right][/tex]

Solution:

The number of shares triples everyday, therefore, the number of shares form a geometric progression, with a common ratio of r = 3, and a first term of a = 2

The function for the number of shares of Ben's post is, tₙ  = a·rⁿ

Which gives;

  • Ben's social media post shares on day tₙ = 2·3ⁿ

Carter's social media posts;

Given;

Number of friends Carter shared his post with = 10 friends

Number of people each of the 10 friends shared with each day = 2 people

Solution;

The exponential function for number of shares received by Carter is therefore, tₙ = 10×2ⁿ

  • Carter's social media post shares on day n: 10 × 2ⁿ

Learn more about exponential functions here:

https://brainly.com/question/1530446

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