Find an approximate equation $\displaystyle y=ab^{x}$ of the exponential curve that contains the given pair of points. Round the value of b to two decimal places.

(0, 256) and (7, 23)

my work:

$\displaystyle 256b^7=23$

$\displaystyle 256^7=\frac{23}{256}$

$\displaystyle b=\sqrt[7]{\frac{23}{256}}$ which is $\displaystyle b=4.7$

Thus, $\displaystyle y=256(4.7)^{x}$

Is this the right answer?