1) Linear model
R(t) = y = at + b
Where t is the year - 2000 (year since 2000)
For year 2006, t = 6; for year 2010, t = 10
Then:
1) 10.7 = a*6 + b
2) 34.2 = a*10 + b
Subtract (1) from (2)
34.2 - 10.7 = 10a -6a
23.5 = 4a
a = 23.5/4 = 5.875
Now from (1) 10.7 = 6a + b => b = 10.7 - 6a = 10.7 - 6*5.875 = - 24.55
Then the resulting model is R(t) = 5.875a - 24.55
2) Exponential model
R(t) = A[B]^t
(1) 10.7 = A[B]^6
(2) 34.2 = A[B]^10
Divide (2) by (1)
[34.2/10.7] = [B]^10 / [B]^6
3.1963 = [B]^4 => B = 1.3371
Now, from (1) 10.7 = A [1.3371]^6 => A = 10.7 / [1.337]^6 = 1.8725
Then, the model is R(t) = 1.8725{1.3371]^t
