Find the equation of the exponential function represented by the table below:
x y
0 2
1 1
2 0.50
3 0.25

Step-by-step explanation:

Exponential Function

When we need to express the exponential relation between two variables, we use the equation

where C, r are constants to be determined by using the given points from the table

For x=0, y=2, thus

We find that C=2

The equation is now

Now we use the point x=1, y=1

We find that

Thus, the equation is

Rearranging

The required equation is

We can easily verify the last two points are also obtained by using the equation

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3