Identify the exponential function for this graph

Option: A is the correct answer.

Step-by-step explanation:

Clearly from the graph we could observe that the graph is a decay exponential function as the graph of the function is decreasing with the increasing value of x.

Hence, the rate has to be less than 1.

So, option: B and D are ruled out as they represent a growth exponential function.

Also from the graph given in the question we could observe that when x=0 the value of y is:

y=4

So, the exponential function that is represented by the graph is:

3√2 units

Step-by-step explanation:

We can see that the line the triangles share bisects the right angle.  This means that each smaller angle is 45°.  

This makes each smaller triangle a 45-45-90 triangle.  This means the relationship between the sides is t, t, t√2; this means that the two legs of the triangle are equivalent and the hypotenuse is equal to the leg multiplied by the square root of 2.  

This means that x, the hypotenuse of the triangle, is 3√2.