Final answer:
The sequence that can be modeled by the equation f(n) = 5 - 2(n-1) is sequence option (c) 5, 3, 1, -1, -3, since it correctly follows the pattern established by the equation.
Step-by-step explanation:
The sequence that could be modeled by the equation f(n) = 5 - 2(n-1) represents a linear function where the starting value is 5 and the common difference is -2.
This means that each subsequent term is 2 less than the previous term.
To find out which of the listed sequences fits this pattern, we can apply the function to the first few integers and see which sequence matches the output.
For n=1: f(1) = 5 - 2(1-1)
= 5 - 0
= 5
For n=2: f(2) = 5 - 2(2-1)
= 5 - 2
= 3
For n=3: f(3) = 5 - 2(3-1)
= 5 - 4
= 1
For n=4: f(4) = 5 - 2(4-1)
= 5 - 6
= -1
For n=5: f(5) = 5 - 2(5-1)
= 5 - 8
= -3
When we compare the results from applying the function to the sequences listed, we find that sequence (c) 5, 3, 1, -1, -3 matches the outputs perfectly.