Verifying the constant elasticity of the demand model Q= aP^b
The problem with your calculations is that you have very big changes in price   

If you made price increases of $1\%$ in price, you would find the quantity fell by about $2\%$ as shown in the table below leading to an elasticity of about $-2$  

If you made the price changes even smaller, the calculated elasticity would get even closer to $2$, and in a sense you are looking for the limit of elasticity as the price change approaches $0$, which will indeed be the constant $b=-2$

 a       b      P       Q=a*P^b pct change Q    pct change P   elasticity

100     -2      1       100.00          
100     -2      1.01     98.03      -1.97%          1%          -1.97
100     -2      2        25.00          
100     -2      2.02     24.51      -1.97%          1%          -1.97
100     -2      3        11.11          
100     -2      3.03     10.89      -1.97%          1%          -1.97
100     -2      4         6.25          
100     -2      4.04      6.13      -1.97%          1%          -1.97
100     -2      5         4.00          
100     -2      5.05      3.92      -1.97%          1%          -1.97