1.
3.
The exponential function representing the spread of Ben's social media post is given by-
f(x)=2(3)^x
4.
4.
The green line represents the social media post of Amber, the orange line represents the social media post of Ben while the purple line represent the social media post of Carter.
5.
6.
7.
Amber's function- f(x)=3(4)^x
For day 3, x = 3. The number of shares Amber's post would have received on day 3 is given by- f(3)=3(4)^x
And for day 10, x = 10. The number of shares Amber's post would have received on day 10 is given by-
f(10)=3(4)^10=3(1,048,576)=3,145,728
Ben's function- f(x)=2(3)^x
For day 3, x = 3. The number of shares Ben's post would have received on day 3 is given by- f(3)=2(3)^3=2(27)=54
And for day 10, x = 10. The number of shares Ben's post would have received on day 10 is given by- f(10)=2(3)^10=2(59,049)=118,098
The black line represents the new function while the green line represents the old function.
The graph of the new function representing Amber's photo share after she mailed copies of her photo to the 45 residents of her grandmother's assisted living facility is the same as the graph of the old function, but the graph of the new function is translated (shifted) up by 45 units.
Based on the result, Amber's post traveled faster.
In an exponential function, the base (growth factor) determines how fast the function grows. The greater the growth factor, the faster the growth of the function.
So, since Amber's growth factor is 4, which is greater than Ben's 3 and Carter's 2, Ambers post traveled faster.
I would want my post to spread faster, so I would prefer a post with fewer friends initially but more shares. Based on the explanations given in question 6 above. The greater the growth factor (in this case: the number of shares), the faster the spread of the function (the faster the spread of the post).
Carter's function- f(x)=10(2)^x
For day 3, x = 3. The number of shares Carter's post would have received on day 3 is given by- f(3)=2(3)^3=2(27)=54
And for day 10, x = 10. The number of shares Carter's post would have received on day 10 is given by- f(10)=2(3)^10=2(59,049)=118,098
2.
The exponential function representing the spread of Carter's social media post is given by-
f(x)=10(2)^x
Step-by-step explanation:
