Answer :
Hence , it is to be quadratic function where a has to be less than zero.
Given that ,
The table contains data on the number of people visiting a historical landmark over a period of one week.
We have to find,
The relationship between the day and the number of visitors.
According to the question,
[tex]y = a\sqrt{x} + b[/tex]
And where x = no. of days = 1
y = no. of visitors = 45
45 = a [tex]\sqrt{1}[/tex] + b
45 = a + b
And When x = 2 and y = 86
86 = [tex]a\sqrt{2} + b[/tex]
Solving the equation for the values of a and b.
From equation 1
45 - a = b
Put the value of b in equation 2
86 = [tex]a\sqrt{2}[/tex] + 45 - a
86 - 45 = [tex]a \sqrt{2} - a[/tex]
41 = a ([tex]\sqrt{2} - 1[/tex] )
[tex]a = \frac{41}{\sqrt{2} - 1 }\\\\a = \frac{41}{0.41}[/tex]
a = 100
Put the value of a = 100
45 = 100 + b
45 - 100 = b
b = -55
The required equation is y = 100[tex]\sqrt{x}[/tex] -55.
When x = 4
[tex]y = 100\sqrt{2} - 55\\\\ y = 100 ( 1.4 ) - 55\\\\y = 140 - 55\\\\y = 85[/tex]
And when x = 5
[tex]y = 100\sqrt{5} - 55\\\\y = 223.5 - 55\\\\y = 168.60[/tex]
y = 168 ( approx )
Therefore, 168 ≠ 158
Since the function rises less and less in later stage , it can not be a first order function.
So, it is to be quadratic function where a has to be less than zero.
For more information about quadratic equation click the link given below.https://brainly.com/question/2263981