Answer :
To determine which type of model best fits the given data, we can analyze the behavior of the number of views over the days.
Given data:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x \, (\text{days}) & 0 & 1 & 2 & 3 & 4 \\ \hline y \, (\text{number of views}) & 3600 & 1800 & 900 & 450 & 225 \\ \hline \end{array} \][/tex]
First, let's look at how the values of \( y \) change as \( x \) increases:
- From day 0 to day 1: \( \frac{1800}{3600} = 0.5 \)
- From day 1 to day 2: \( \frac{900}{1800} = 0.5 \)
- From day 2 to day 3: \( \frac{450}{900} = 0.5 \)
- From day 3 to day 4: \( \frac{225}{450} = 0.5 \)
We notice that each successive value of \( y \) is half (or 0.5 times) the previous value. This consistent ratio suggests that the number of views is decreasing by the same factor each day.
In an exponential decay model, the quantity decreases by a consistent factor over equal intervals of time. The pattern here fits that description, as each day's view count is 50% (or a factor of 0.5) of the previous day's count.
Since the number of views decreases by a consistent factor (0.5) each day, the data fits an Exponential decay model.
Given data:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x \, (\text{days}) & 0 & 1 & 2 & 3 & 4 \\ \hline y \, (\text{number of views}) & 3600 & 1800 & 900 & 450 & 225 \\ \hline \end{array} \][/tex]
First, let's look at how the values of \( y \) change as \( x \) increases:
- From day 0 to day 1: \( \frac{1800}{3600} = 0.5 \)
- From day 1 to day 2: \( \frac{900}{1800} = 0.5 \)
- From day 2 to day 3: \( \frac{450}{900} = 0.5 \)
- From day 3 to day 4: \( \frac{225}{450} = 0.5 \)
We notice that each successive value of \( y \) is half (or 0.5 times) the previous value. This consistent ratio suggests that the number of views is decreasing by the same factor each day.
In an exponential decay model, the quantity decreases by a consistent factor over equal intervals of time. The pattern here fits that description, as each day's view count is 50% (or a factor of 0.5) of the previous day's count.
Since the number of views decreases by a consistent factor (0.5) each day, the data fits an Exponential decay model.
