Question

Find the equation of the exponential function represented by the table below:

Answer 1

Answer:

$y=2^{1-x}$

Step-by-step explanation:

Exponential Function

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

$y=Cr^{x}$

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

For x=0, y=2, thus

$2=C.r^{0}=C$

We find that C=2

The equation is now

$y=2r^{x}$

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

$1=2r$

We find that

$\displaystyle r=\frac{1}{2}$

Thus, the equation is

$\displaystyle y=2\left(\frac{1}{2}\right)^{x}$

Rearranging

$y=2(2)^{-x}=2^{1-x}$

The required equation is

$y=2^{1-x}$

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