Pre-Calc Help Please Find the exponential function f(x)=Ca^x whose graph goes through the points (0,3) and (2,12). Thank you.?

y = f(x) = C a^x

When x = 0, y = 3 :
3 = C a^0
C = 3

Then, y = f(x) = 3 a^x

When x = 2, y = 12 :
12 = 3 a^2
a^2 = 4
a^2 = 2^2
a = 2

Then, f(x) = 3 * 2^x

Let f(x) = y
Hence
y = Ca^x
for the point (0,3)
3 = Ca^(0)
NB Anything to the power 'o' equals '1'
Hence
3 = C(1)
C = 3

When C = 3
y = 3a^x
12 = 3(a^2)
a^2 = 12/3 = 4
a^2 = 4
a = +/- 2
Hence the equation becomes
y = 3(2^x)
f(x) = 3(2^x)

f(x) = Ca^x

f(0) = 3 = Ca^0

= C

f(2) = 12 = 3a^2

3a^2 = 12

a^2 = 4

a = ± 2

f(x) = 3*(2)^x, 3*(-2)^x