Question

The graph of an exponential function passes through (2,−12) and (3,−24). Find the exponential function that describes the graph.

Answer 1

no fancy math here, just some reasoning with words. I just feel like it

for one step in x-direction the value of the function doubles, so the common factor is 2.

so let's trace it back

(1,-6)

(0, -3)

For an exponential function the y-intercept is the "initial value".

do let's write is as a function

$y = - 3 \times {2}^{x}$

you could also use the points and plug their numbers into the general formula, but I felt this explanation could give you more understanding, since it's meant to be more intuitive.

hope it helps