Answered

Get the information you need with the help of IDNLearn.com's extensive Q&A platform. Get comprehensive and trustworthy answers to all your questions from our knowledgeable community members.

The table shows the number of views, in millions per day, of a music video that is viewed on two different websites. If the pattern for each website continues, which website will have more views after one month and why?

Views of a Music Video:

\begin{tabular}{|c|c|c|}
\hline Time (days) & \begin{tabular}{c}
Website [tex]$A$[/tex] \\
(in millions)
\end{tabular} & \begin{tabular}{c}
Website B \\
(in millions)
\end{tabular} \\
\hline 0 & 0 & 1 \\
\hline 1 & 1 & 3 \\
\hline 2 & 10 & 9 \\
\hline 3 & 29 & 27 \\
\hline
\end{tabular}

A. Website [tex]$A$[/tex], because the number of views is growing at a cubic rate.
B. Website [tex]$A$[/tex] and [tex]$B$[/tex] will have the same number of views, because they will both reach a maximum number of viewers.
C. Website [tex]$B$[/tex], because the number of views is growing exponentially.
D. Website [tex]$A$[/tex], because the number of views is growing exponentially.

Sagot :

GinnyAnsweridn
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.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.