The number of visitors to a park is expected to follow the function v(x) = 5(x − 1), where x is the number of days since opening. On the first day, there will be a ceremony with 20 people in attendance. What is the function that shows total visitors, including the ceremony?

For this case, the first thing we must do is define variables.
We have then:
x: number of days
v (x): total number of visitors including the ceremony.
The function that represents the problem is:
[tex]v (x) = 5 (x - 1) + k [/tex]
Where,
k: number of visitors on the first day.
To find the value of k we substitute the following pair ordered in the function:
[tex](x, v (x)) = (1, 20) [/tex]
We have then:
[tex]20 = 5 (1 - 1) + k 20 = 5 (0) + k 20 = 0 + k 20 = k[/tex]
Then, the function is:
[tex]v (x) = 5 (x - 1) + 20 [/tex]
Answer:
the function that shows total visitors, including the ceremony is:
[tex]v (x) = 5 (x - 1) + 20[/tex]