To determine the correct conclusion about the number of subscribers to the newspaper, we need to analyze the given function:
[tex]\[ f(t) = 75 \times (0.95)^t \][/tex]
Here's how we can interpret this function step-by-step:
1. Understand the Mathematical Form:
- The general form of an exponential decay function is [tex]\( f(t) = A \times (r)^t \)[/tex], where:
- [tex]\( A \)[/tex] is the initial quantity (here, 75 subscribers).
- [tex]\( r \)[/tex] is the decay factor (here, 0.95).
- [tex]\( t \)[/tex] is the time in years.
2. Analyze the Decay Factor:
- We see that the base of the exponent, [tex]\( r = 0.95 \)[/tex], is less than 1.
3. What Does [tex]\( 0.95 \)[/tex] Mean?:
- The base [tex]\( 0.95 \)[/tex] indicates that each year, the number of subscribers retains 95% of the previous year's subscribers.
- In other words, 95% retention means there's a 5% reduction each year. This is because 100% - 95% = 5%.
4. Conclusion:
- Since [tex]\( f(t) = 75 \times (0.95)^t \)[/tex] shows a reduction (decay) of subscribers by a factor of 0.95 each year, it signifies a 5% decrease annually in the number of subscribers.
Therefore, the correct conclusion is:
It decreased by 5% every year.
