Consider $k(x)=3(2)^{x+2}$.  

1. Describe the transformation from $y=2^x$ to $y=k(x)$.

   Hint (a):

   It is vertically stretch by a factor of ____.
   It is shifted ____ $2$ units.

2. What is the $y$-intercept of $y=k(x)$?

   Step (b):

   Solve $y=3(2)^{0+2}$.

3. Write the equation of an exponential function in the form $m(x)=A(2)^x$ with the same $y$-intercept as part (b).

   Step (c):

   Solve: $y$-intercept $=A(2)^0$

4. Is $m(x)=k(x)$? Justify your answer algebraically.