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1.Write an exponential function to represent the spread of Ben's social media post.

2.Write an exponential function to represent the spread of Carter's social media post.

3.Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.

4.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.

5.If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?

6.Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?

7.If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.

1Write An Exponential Function To Represent The Spread Of Bens Social Media Post2Write An Exponential Function To Represent The Spread Of Carters Social Media P class=

Sagot :

The rate of growth of the exponential function is determined by the

growth factor.

The correct responses are;

  • 1. Exponential function for Ben's post shares is f(x) = 2·3ˣ
  • 2. The exponential function for Carter's post shares is f(x) = 10·2ˣ
  • 3. Please find attached the graph of the exponential function of each of the students posts shares
  • 4. The number of shares received by Amber
  • On Day 3 = 192 shares
  • On Day 10 = 3,145,728 shares

  • The number of shares received by Ben
  • On Day 3 = 54 shares
  • On Day 10 = 118,098 shares

  • The number of shares received by Carter
  • On Day 3 = 80 shares
  • On Day 10 = 10,240 shares

  • 5. The graph of the new function is a translation of the graph of the original function 45 units in the upward direction.

  • 6. Based on the result, the post that travels fastest is Amber's post that has the highest growth factor of 4.

  • 7. A post with fewer friends and more shares is preferable.

Reasons:

1. The general form of the exponential function is; Shares, f(x) = a·bˣ

On day 0, we have; x = 0, f(0) = 2, which gives;

f(0) = a·b⁰ = a = 2

a = 2

At x = 1, f(1) = 6

f(1) = a·b¹ = 2 × b¹ = 6

∴ b = 6 ÷ 2 = 3

b = 3

Which gives;

The the exponential function for Ben's social media post as; f(x) = 2·3ˣ

2. The number of friends with which Carter shares his post = 10 friends

Number of people each of the 10 friends share their post = 2 people

Which gives;

The initial value, a = 10

The growth factor, b = 2

The exponential function is therefore, f(x) = 10·2ˣ

3. Please find attached the graph of each of the exponential functions created with MS Excel

4. On Day 3, we have;

The number of shares Amber's post receives, f(3) = 3×4³ = 192 (shares)

For Ben, we have, f(3) = 2 × 3³ = 54 (shares)

Carter's posts gives, f(3) = 10 × 2³ = 80 (shares)

On Day 10, we have;

The number of shares Amber's post receives, f(10) = 3 × 4¹⁰ = 3,145,728 (shares)

Ben's post gets, f(10) = 2 × 3¹⁰ = 118,098 (shares)

Carter's post gets f(10) = 10 × 2¹⁰ = 10,240 (shares)

5. The new function is f(x) = 3·(4)ˣ + 45

The function of the original graph of Amber's photo share is f(x) = 3·(4)ˣ

The difference is; 3·(4)ˣ + 45 - 3·(4)ˣ = 45

Therefore, the values of the new function are 45 more than the values of the original function

Therefore;

The graph of the new function is translated upwards by 45

6. Based on the analyses of the result, the student posts that travel the fastest is the one with the highest growth factor, which is Amber's post

7. Given that the aim is to get more social, the best option is to have more shares and fewer friends.

Learn more about exponential function here:

https://brainly.com/question/1528738

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