Answer:
The function is:
[tex]f(x)=3 \cdot 2^x[/tex]
[tex]C=3[/tex]
[tex]A=2[/tex]
Step-by-step explanation:
[tex]f(x)=C\cdot A^x[/tex]
Let's plug in the first point (0,3):
[tex]f(0)=C \cdot A^0[/tex]
[tex]3=C\cdot 1[/tex]
[tex]3=C[/tex]
So we have:
[tex]f(x)=3 \cdot A^x[/tex]
Let's use the other point (2,12):
[tex]f(2)=3 \cdot A^2[/tex]
[tex]12=3 \cdot A^2[/tex]
Divide both sides by 3:
[tex]\frac{12}{3}=A^2[/tex]
[tex]4=A^2[/tex]
Square root both sides:
[tex]\pm \sqrt{4}=A[/tex]
[tex]\pm 2=A[/tex]
Exponential functions have positive bases so [tex]A=2[/tex].
The function is:
[tex]f(x)=3 \cdot 2^x[/tex]
[tex]C=3[/tex]
[tex]A=2[/tex]
