Question

Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.

Student
Amber
Ben
Carter
Description
Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function.
Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day.
Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares
f(x) = 3(4)x

Day
Number of Shares
0:2
1:6
2:18





Carter shared his post with 10 friends, who each share with only 2 people each day.

Write an exponential function to represent the spread of Ben's social media post.
Ben shared his post with two friends. Each of those friends shares with 3 more everyday, so the number of shares triples each day.

Answer 1

Answer:

First write the two binomials in a row separated by using multiplication sign. 2. Multiply each term of one binomial with each term of the other. 3. In the product obtained, combine the like terms and then add the like terms.The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables). Here, the term with the largest exponent is , so the degree of the whole polynomial is 6.Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency to emphasize the contrast to spatial frequency, and ordinary frequency to emphasize the contrast to angular frequency. Frequency is measured in hertz which is equal to one per second. 

Answer 2

The number of shares received by the posts (Day 3, Day 10) of Amber, Ben and Carter are (192, 3145728), (54, 118098), and (80, 10240), respectively.

Given:

The number of people with whom Amber shares the post = 3.

The function that represents the spread of Amber's post is: $f(x) = 3(4)^x$.

The number of people with whom Ben shares the post = 2.

The number of people to which Ben's friends share the post each day = 3.

The number of people with whom Carter shares the post = 10.

The number of people with whom Carter's friends share the post each day = 2.

To Find:

We have to find out the number of shares received by each student's post on Day 3 and then on Day 10.

Solution:

Let "m" be the number of friends to which a person share the post and  and each one of those people sent it to "r" other people the first day. Each one of this "mr" amount of friends then shares the post with "r" other people on the second day and so on each day.

∴, The general exponential function can be written as,

$f(x) = m(r)^x$,

where $f(x)$ is the amount of people reached by the post in the $x^{th}$ day.

Given that, the function that represents the spread of Amber's post is: $f(x) = 3(4)^x$.

Similarly, we can write the exponential functions that represents the spread of Ben's and Carter's post as follows.

The function that represents the spread of Ben's post is: $f(x) = 2(3)^x$.

The function that represents the spread of Carter's post is: $f(x) = 10(2)^x$.

Substituting x = 3 in the exponential functions, we get the number of shares received by the posts on Day 3.

The number of shares for Amber = $f(3) = 3(4)^3 = 192.$

The number of shares for Ben = $f(3) = 2(3)^3 = 54.$

The number of shares for Amber = $f(3) = 10(2)^3 = 80.$

Substituting x = 10 in the exponential functions, we get the number of shares received by the posts on Day 10.

The number of shares for Amber = $f(10) = 3(4)^{10} = 31,45,728.$

The number of shares for Ben = $f(10) = 2(3)^{10} = 1,18,098.$

The number of shares for Amber = $f(10) = 10(2)^{10} = 10,240.$

Hence, the number of shares received by the posts of Amber, Ben and Carter are:

Amber - Day 3 = 192, Day 10 = 31,45,728

Ben - Day 3 = 54, Day 10 = 1,18,098

Carter - Day 3 = 80, Day 10 = 10,240.

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