An exponential function passes through the points $\left(2, 36\right)$ and $\left(4, 81\right)$.

1. Is the function increasing? Explain.

   Answer (a):

   As $x$ increases from $2$ to $4$, $y$ increases from $36$ to $81$. Thus, the function is increasing.

2. Find the exponential function that passes through the two given points.

   Hint (b):

   Use the form: $y = Ab^{x}$
   Substitute the coordinates of the points for $\left(x, y\right)$ to obtain two equations and solve for $A$ and $b$.

3. If the function you found in part (b) was shifted so that it has a horizontal asymptote of $y = 20$, what would the new function be?

   Hint (c):

   Add a $+ 20$ to the function found in part (b).

   Use the eTool below to visualize this problem.
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