# How do you find the exponential function f(x) = Ca^x whose graph has the given points (0,2) and (3,54)?

Oct 3, 2016

$f \left(x\right) = 2 \left({3}^{x}\right)$

#### Explanation:

$f \left(0\right) = 2 = C {a}^{0}$

$C = 2$

$f \left(3\right) = 54 = 2 {a}^{3}$

$27 = {a}^{3}$

$a = \sqrt[3]{27}$

$a = 3$

$f \left(x\right) = 2 \left({3}^{x}\right)$