The function [tex]\( f(x) = 2577(1.5)^x \)[/tex] models the number of visitors to a website [tex]\( x \)[/tex] years after its launch.
To determine the relationship between the number of visitors each year, we need to understand the growth factor in the function.
The form of the function [tex]\( f(x) = a \cdot b^x \)[/tex] tells us that:
- [tex]\( a = 2577 \)[/tex] is the initial number of visitors at [tex]\( x = 0 \)[/tex].
- [tex]\( b = 1.5 \)[/tex] is the growth factor, meaning every year, the number of visitors is multiplied by 1.5.
This shows that each year [tex]\( x \)[/tex], the number of visitors [tex]\( f(x) \)[/tex] is 1.5 times the number of visitors from the previous year [tex]\( f(x-1) \)[/tex].
So, the number of visitors each year is [tex]\( 1.5 \)[/tex] times the number of visitors the year before.
Thus, the correct answer is:
D. 1.5 times
