Answer :
Let's analyze Sharon's data on the number of subscribers to the fashion magazine from the year 2000 to 2004:
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of Years Since 2000} & \text{Number of Subscribers} \\ \hline 0 & 25,000 \\ \hline 1 & 20,000 \\ \hline 2 & 16,000 \\ \hline 3 & 12,800 \\ \hline 4 & 10,240 \\ \hline \end{tabular} \][/tex]
The data indicates that the number of subscribers decreases over time. The pattern suggests an exponential decay since each year sees a percentage decrease rather than a consistent subtraction.
Given this, let's answer each part of the question:
1. The number of subscribers is:
- Looking at the pattern in the table, it is observed that the decrease follows an exponential function rather than a linear one or any other form. Each year, the number of subscribers reduces by a consistent percentage.
Answer: Exponentially decreasing
2. As the number of years since 2000 increases, the number of subscribers to the magazine will approach:
- Exponential decay means that as time goes on, the quantity will approach a limit asymptotically, which in the context of subscribers means that if the trend continues indefinitely, the number will approach zero.
Answer: 0
So the complete answers are:
The number of subscribers is exponentially decreasing.
As the number of years since 2000 increases, the number of subscribers to the magazine will approach 0.
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of Years Since 2000} & \text{Number of Subscribers} \\ \hline 0 & 25,000 \\ \hline 1 & 20,000 \\ \hline 2 & 16,000 \\ \hline 3 & 12,800 \\ \hline 4 & 10,240 \\ \hline \end{tabular} \][/tex]
The data indicates that the number of subscribers decreases over time. The pattern suggests an exponential decay since each year sees a percentage decrease rather than a consistent subtraction.
Given this, let's answer each part of the question:
1. The number of subscribers is:
- Looking at the pattern in the table, it is observed that the decrease follows an exponential function rather than a linear one or any other form. Each year, the number of subscribers reduces by a consistent percentage.
Answer: Exponentially decreasing
2. As the number of years since 2000 increases, the number of subscribers to the magazine will approach:
- Exponential decay means that as time goes on, the quantity will approach a limit asymptotically, which in the context of subscribers means that if the trend continues indefinitely, the number will approach zero.
Answer: 0
So the complete answers are:
The number of subscribers is exponentially decreasing.
As the number of years since 2000 increases, the number of subscribers to the magazine will approach 0.
