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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 <u>f(x) = 2·3ˣ</u>
- 2. The exponential function for Carter's post shares is <u>f(x) = 10·2ˣ</u>
- 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 = <u>192 shares</u>
- On Day 10 = <u>3,145,728 shares</u>
- The number of shares received by Ben
- On Day 3 = <u>54 shares</u>
- On Day 10 = <u>118,098 shares</u>
- The number of shares received by Carter
- On Day 3 = <u>80 shares</u>
- On Day 10 = <u>10,240 shares</u>
- 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 <u>fewer friends and more shares is preferable</u>.
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; <u>f(x) = 2·3ˣ</u>
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, <em>b</em> = 2
The exponential function is therefore, <u>f(x) = 10·2ˣ</u>
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 = <u>192 (shares)</u>
For Ben, we have, f(3) = 2 × 3³ = <u>54 (shares)</u>
Carter's posts gives, f(3) = 10 × 2³ = <u>80 (shares)</u>
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 = <u>118,098 (shares)</u>
Carter's post gets f(10) = 10 × 2¹⁰ = <u>10,240 (shares)</u>
5. The new function is f(x) = 3·(4)ˣ + 45
The function of the original graph of Amber's photo share is <u>f(x) = 3·(4)ˣ</u>
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 <u>more shares and fewer friends</u>.
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