Which of these exponential functions goes through the points (1, 12) and (2, 36)? a.) f(x) = 4(3)−x b.) f(x) = 3(4)−x c.) f(x) = 3(4)x d.) f(x) = 4(3)x

Option D is correct

The exponential function is:

Explanation:

An exponential function is in the general form is:

.                ......[1]

Given the points  (1,12) and (2, 36).

For the point (1,12),

Plug in x = 1 and y =12 in [1]; we get

or

12 =ab                  ......[2]

Now, for the point (2, 36);

Plug in x= 2 and y =36 in [1];

                  ......[3]

Divide equation [3] by equation [2], we have

Simplify:

Substitute the value of b in equation [2], to solve for a;

Divide both side by 3 we get;

simplify:

Then, put these a and b values in [1]; we get

The exponential function as:

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.