Help with chemistry - Arrhenius Equation

Question

I am aware of the derivations of the Arrhenius equation but for some reason I am doing something wrong along the way and I need to figure this out! Could someone please show me the steps??

 

Question: 

 

A reaction is found to have an activation energy of 38.0 kJ/mol. If the rate constant for this reaction is 1.60 ×
102 M-1s-1 at 249 K, what is the rate constant at 436 K?

 

Please help me if you can!

Answer 1

ln(k₁/k₂ ) = Ea/R(1/T₁ - 1/T₂ )

 

ln(1.6*10²/k₂) = (38.0*1000)/8.314(1/436 - 1/249)

                       = 4570.6(-0.001722)

                       = -7.873

 (1.6*10²/k₂)    = e^-7.873  = 0.0003810

               k₂        = 1.6*10² /0.0003810 = 4.20*10⁵