Find a and c in the equation Find a and c in the equation
$$y=ca^x$$
when it is given that $x = \frac{1}{2}$ gives $y = 6$ and $x = 2$ gives $y = 162$
I already tried to solve when $6=ca^{\frac{1}{2}}$ and managed to get $a=\frac{36}{c^2}$ and when I insert $a$ in the equation $6=c\cdot \left(\frac{36}{c^2}\right)^{\frac{1}{2}}$, then I end up getting $0$ for $c$. Would appreciate help :)

Suppose we have $y=ca^{x}$. Then substituting the points $(x,y)=(\frac{1}{2},6)$ and $(x,y)=(2,162)$ gives $$6=ca^{\frac{1}{2}}$$
$$162=ca^{2}$$
Dividing the two we obtain $a^{\frac{3}{2}}=\frac{162}{6}=27$ so $a=9$. Now substituting into the first we obtain $$6=c(9)^{\frac{1}{2}}=3c$$
so $c=2$. Thus we have $y=2\cdot 9^{x}$.
