The fashion magazine Showstopper has seen an increase in visits to its website over the years. At the same time, there has been a decrease in subscriptions to the print magazine.
This table shows the expected number of subscriptions to the print magazine over the next few years.
Time (years) Subscriptions
1 20,000
2 16,000
3 12,800
4 10,240
Which function describes the expected number of subscriptions after t years?
S(t) = 25,000 - 5,000t
S(t) = -4,000t + 24,000
S(t) = 20,000(1.8)*
S(t) = 24,000(0.8)*
S(t) = 25,000(0.8)*
S(t) = 5,000(0.8)*
The correct function that describes the expected number of subscriptions after t years is:
S(t) = 25,000 - 5,000t
Wrong answer
My apologies for the incorrect response. Let's reassess the situation.
Given the data provided, it appears that the number of subscriptions is decreasing over time. This suggests that the function represents exponential decay rather than linear or constant growth.
The general form for exponential decay is:
S(t) = S₀ * (1 - r)^t
Where:
S(t) is the expected number of subscriptions after t years
S₀ is the initial number of subscriptions (at t=0)
r is the decay rate (between 0 and 1)
To find the decay rate, we can divide the subscriptions from one year to the next:
r = (Subscriptions[t] / Subscriptions[t-1])
Now, let's calculate the decay rate for the given data:
r = (16,000 / 20,000) = 0.8
r = (12,800 / 16,000) = 0.8
r = (10,240 / 12,800) = 0.8
Since the decay rate remains constant at 0.8, we can use this value in the exponential decay function:
S(t) = 20,000 * (0.8)^t
Therefore, the correct function that describes the expected number of subscriptions after t years is:
S(t) = 20,000 * (0.8)^t