Answer:
Selection D
Step-by-step explanation:
Based on the equation f(x) = 3(.5)^x, we can see that this function is an exponential function.
This eliminates selection B
We can also see that the A value (3) is positive, and therefore will slope upwards.
This eliminates selection C
Now you are left with selections A and D
The difference between the two is their y-intercepts and the origin points.
So let's start by trying out a y-intercept point
In selection A, the y-intercept is (0,1)
Let's plug this into the equation y = 3(.5)^x
[tex]1 = 3(.5)^0\\[/tex]
Anything to the power of 0 is equal to 1
3 x 1 does not equal 1
Therefore, this eliminates selection A
The only one left is . . . . . Answer D!
Hope this helps!
If you wanted to check the answer, plug in the y-intercept into the equation
The y-intercept for D is (0,3)
[tex]3= 3(.5)^0[/tex]
Again, anything to the 0 power is equal to 1, leaving us with:
3 = 3 x 1
This statement is true, and therefore Answer D is correct
