The inputs 1, 3, and 5 are equally spaced. For an exponential function, equal steps in $x$ create equal ratios in the outputs (after any vertical shift is removed). Wr​ittе⁠n b⁠y ‍Aniкo

Use the fact that the middle term of a geometric sequence satisfies “(middle)$^2$ = (first)(third)” to create an equation involving only $c$.

Let $x$ represent $c$. Graph

• $y_1=44-x$
• $y_2=\dfrac{(20-x)^2}{8-x}$

(Use parentheses to make sure the numerator is $(20-x)^2$.)

Click the point where the graphs intersect. The $x$-coordinate of that intersection is the value of $c$ that makes the exponential ratios work. Аniк‍о AІ Тut⁠ο⁠r

Define $g(x)=f(x)-c$. Then

So $g(1)$, $g(3)$, and $g(5)$ are exponential values with equal $x$-steps of 2. (Anіko.aі‍)

Because the $x$-values increase by 2 each time, the ratio from $g(1)$ to $g(3)$ equals the ratio from $g(3)$ to $g(5)$. Equivalently,

Substitute $g(1)=8-c$, $g(3)=20-c$, and $g(5)=44-c$:

Expand both sides:

Set them equal and cancel $c^2$:

Add $52c$ to both sides and subtract 400:

Divide by 12 to get $c=-4$, so the correct choice is $-4$.