To determine which website will have more views after one month (30 days), we need to analyze the growth patterns for Website A and Website B based on the information given in the table.
### Analyzing the Growth Patterns:
#### Website A:
- On day 0: 0 million views
- On day 1: 1 million views
- On day 2: 10 million views
- On day 3: 29 million views
We notice the growth in views isn't linear. To hypothesize a pattern, we consider a polynomial (cubic) growth for Website A, which can be modeled as:
[tex]\[ V_A(t) = at^3 + bt^2 + ct + d \][/tex]
We use the given data points to find the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex]. Although a detailed calculation isn't directly provided here, initial fits and calculations suggest that the data fits well with a polynomial (cubic) pattern, thereby growing very quickly as time progresses.
#### Website B:
- On day 0: 1 million views
- On day 1: 3 million views
- On day 2: 9 million views
- On day 3: 27 million views
We observe that each number of views is three times the previous day's views:
[tex]\[ 1, 3, 9, 27 \][/tex]
This exponential pattern can be modeled as:
[tex]\[ V_B(t) = a \cdot e^{bt} \][/tex]
where [tex]\(e\)[/tex] is the base of the natural logarithm. Given the exponential growth (doubling or tripling patterns), we see a rapid increase in views.
### Which will have more views after one month (30 days)?
#### Website A:
Given the cubic growth pattern:
[tex]\[ V_A(t) \approx at^3 \][/tex]
The views at 30 days would be:
[tex]\[ V_A(30) \approx a \cdot 30^3 \][/tex]
#### Website B:
Given the exponential growth pattern:
[tex]\[ V_B(t) = 1 \cdot 3^{t} \, \, \text{or} \, \, V_B(t) = a \cdot e^{bt} \][/tex]
At 30 days:
[tex]\[ V_B(30) = 3^{30} \][/tex]
Comparing cubic growth and exponential growth, exponential growth tends to outpace cubic growth significantly over larger periods of time. The exponential term [tex]\(3^{30}\)[/tex] grows much faster than [tex]\(30^3\)[/tex].
### Conclusion:
Website B will have more views after one month (30 days) because the number of views is growing exponentially. Exponential functions grow much faster than any polynomial function over the same period.
