If the current is cut in half and the resistance is increased by a factor of three, how will the power be affected?

a. the power will increase to 150 percent of its previous value.
b. the power will decrease to 75 percent of its previous value.
c. the power will increase to 450 percent of its previous value.
d. the power will increase to 133 percent of its previous value.

One formula for the power dissipated in an electric circuit is

         Power  =  (current)² x (resistance) .

I think that's the one we should use, because it has exactly
all of the quantities that we know or need to find.

OK.       
               Original power  =  (original current)² x (original resistance)
and
               New power  =  (new current)²  x  (new resistance)

                                 =  (0.5 x old current)² x (3 x old resistance)

                                 = (0.25) (old current)² x (3) (old resistance)

                                 =  (0.75) (original current)² (original resistance)

                                 =  (0.75) (original power) .

Summary:        New power  =  (0.75) (original power)

That looks just like
choice B: 
                 The power will decrease to 75 percent of its previous value.