Arrhenius equation

The rate coefficient (k) for a particular reactions is $1.3\times10^{-4}$ M$^{-1}$ s$^{-1}$ at 100°C, and $1.3\times10^{-3}$ M$^{-1}$ s$^{-1}$ at 150°C. What is the energy of activation ($E_A$) (in kJ) for this reaction ? (R = molar gas constant = 8.314 JK$^{-1}$ mol$^{-1}$)

Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is

For a first order reaction A → P, the temperature (T) dependent rate constant ($k$) was found to follow the equation $\log k=-(2000)\dfrac1T+6.0$. The pre-exponential factor A and the activation energy $E_a$, respectively, are