Question

Which of the following exponential functions goes through the points (1, 12) and (2, 36)?

f(x) = 4(3)−x
f(x) = 3(4)−x
f(x) = 3(4)x
f(x) = 4(3)x

Answer 1

`f(x)=4(3^x)`

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:

`a^(-n)=(1)/(a^n)`

First function:

`f(x)=4(3^(-x) )=(4)/(3^x)`

For the point (1,12)

`f(1)=(4)/(3^1) =(4)/(3) \\eq12`

This function doesn't satisfy one of the conditions.

Second function:

`f(x)=3(4^(-x) )=(3)/(4^x)`

For the point (1,12)

`f(1)=(3)/(4^1) =(3)/(4) \\eq12`

This function doesn't satisfy one of the conditions.

Third function:

`f(x)=3(4^x)`

For the point (1,12)

`f(1)=3(4^1)=3*4=12`

For the point (2,36)

`f(2)=3(4^2)=3*16=48\\eq36`

This function doesn't satisfy one of the conditions.

Fourth function:

`f(x)=4(3^x)`

For the point (1,12)

`f(1)=4(3^1)=4*3=12`

For the point (2,36)

`f(2)=4(3^2)=4*9=36`

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)

Answer 2

Its f(x) = 4(3)^x
As (x=1, y=12), you insert 1 into the variable and its from, 4 x (3)^1 = 12. Same as (x=2, y=36), it becomes 4 x (3)^2 = 36.