Finding an Equation of Nonlinear Data I've been really rusty on math. So excuse me if I sound dumb.
I am trying to find equation for the data below:
x   y
67  0.055
68  
69  
70  
71  
72  
73  
74  
75  
76  
77  
78  
79  
80  
81  
82  
83  
84  
85  0.0275
86  
87  
88  
89  
90  
91  
92  
93  
94  
95  
96  
97  
98  
99  
100 
101 
102 
103 0.01375

What would be the approach to solve this? I am trying to find the values for y.
EDIT: the x values are temp in °F and the y value @ 85 is calculated. The top and bottom values for y are double and half the value of y @ 85.
 A: If there is a systematic reason that the $y$ value is cutting in half every $18$ degrees, then this relationship is exponential. (You can also check out the wikipedia article on half-life.) In this case you can model the relationship by the equation
$$y = 0.0275 \times 0.5^{(x-85)/18}$$
(Alternatively, $y = 0.055 \times 0.5^{(x-67)/18}$ or $y = 0.01375 \times 0.5^{(x-103)/18}$; they are all equivalent.)
The logic is that, since your $y$ is multiplying by $0.5$ every time $x$ increases by $18$ degrees, it must be multiplying by $0.5^{1/18}$ every time $x$ increases by a single degree, so that after $18$ degrees it has multiplied by $(0.5^{1/18})^{18} = 0.5$.
In my first equation, I picked one of the values you gave, $0.0275$, which was the value at $x=85$; then if $x$ is more than $85$, $x-85$ is the number of degrees beyond $85$, so $0.0275$ will have to be multiplied by $0.5^{1/18}$ $x-85$ times, i.e. multiplied by $(0.5^{1/18})^{x-85} = 0.5^{(x-85)/18}$. This is where the formula came from. Similar logic works if $x$ is less than $85$. And the other two equations I gave come from applying the same logic to the other two known points.
