Answer :
Answer:
The model for V(t) ,the number of views, t ,months after it's uploaded, best fits the data is [tex],V(t)=50(6.25)^t[/tex]
Step-by-step explanation:
Time (months) Views
0 50
2 313
4 1950
6 12,210
8 76,300
10 476,800
[tex](x_1,y_1)=(0,50)\\(x_2,y_2)=(2,313)\\(x_3,y_3)=(4,1950)[/tex]
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope = \frac{313-50}{2-0}[/tex]
Slope =131.5
[tex]Slope = \frac{y_3-y_2}{x_3-x_2}[/tex]
[tex]Slope = \frac{1950-313}{4-2}[/tex]
Slope =818.5
Since the slope is not same . So, it is not a linear relationship
[tex]\frac{y_2}{y_1}=\frac{313}{50}=6.25\\\frac{y_3}{y_2}=\frac{1950}{313}=6.25[/tex]
Since the ratio between the consecutive outputs is same so, it is exponential relationship.
Formula : [tex]y=ab^t[/tex]
Where a is the initial value = 50
b = rate of change = 6.25
The model for V(t) ,the number of views, t ,months after it's uploaded, best fits the data
So[tex],V(t)=50(6.25)^t[/tex]
