Question

Scenario

Answer 1

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;

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

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:

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