Once you know $A$, substitute it and $x=1$ into $f(x)=A\cdot r^x$ and use the fact that $f(1)=18$ to form an equation involving only $r$.

Your equation should look like $12r=18$. How do you isolate $r$ in this equation?

After you get $r=18/12$, reduce the fraction completely and then convert it to a decimal to compare with the answer choices.

In a Desmos expression line, type 18/12 (or 18÷12) and press Enter. The numerical result shown is the value of $r$ from the equation $12r=18$.

The function is $f(x)=A\cdot r^x$. When $x=0$,

We are told $f(0)=12$, so $A=12$.

Now use $f(1)=18$.

When $x=1$,

Substitute $A=12$ and $f(1)=18$:

Solve for $r$ by dividing both sides by $12$:

Simplify $\frac{18}{12}$ by dividing numerator and denominator by $6$:

So the value of $r$ is $1.5$, which corresponds to choice A.