Answer:
[tex]f(x)=4(3^x)[/tex]
Step-by-step explanation:
Let's evaluate the functions for every given point, so, we can conclude which of them satisfy the conditions. But first, keep in mind the following:
[tex]a^{-n}=\frac{1}{a^n}[/tex]
First function:
[tex]f(x)=4(3^{-x} )=\frac{4}{3^x}[/tex]
For the point (1,12)
[tex]f(1)=\frac{4}{3^1} =\frac{4}{3} \neq12[/tex]
This function doesn't satisfy one of the conditions.
Second function:
[tex]f(x)=3(4^{-x} )=\frac{3}{4^x}[/tex]
For the point (1,12)
[tex]f(1)=\frac{3}{4^1} =\frac{3}{4} \neq12[/tex]
This function doesn't satisfy one of the conditions.
Third function:
[tex]f(x)=3(4^x)[/tex]
For the point (1,12)
[tex]f(1)=3(4^1)=3*4=12[/tex]
For the point (2,36)
[tex]f(2)=3(4^2)=3*16=48\neq36[/tex]
This function doesn't satisfy one of the conditions.
Fourth function:
[tex]f(x)=4(3^x)[/tex]
For the point (1,12)
[tex]f(1)=4(3^1)=4*3=12[/tex]
For the point (2,36)
[tex]f(2)=4(3^2)=4*9=36[/tex]
This function satisfies all conditions.
Therefore, since the fourth function satisfies all conditions, we can conclude it is the function which goes through the points (1, 12) and (2, 36)
