Question

y=4 times 1/2 to the power of xi need help putting it into a table

Answer 1

SOLUTION

We want to make a table for

$y=4(\frac{1}{2})^x$

Let us take values of x from -2 to 2

So for x = -2, we have

$\begin{gathered} y=4(\frac{1}{2})^{-2} \\ y=4\times4 \\ y=16 \end{gathered}$

For x = -1, we have

$\begin{gathered} y=4(\frac{1}{2})^x \\ y=4(\frac{1}{2})^{-1} \\ y=4\times2 \\ y=8 \end{gathered}$

For x = 0, we have

$\begin{gathered} y=4(\frac{1}{2})^x \\ y=4(\frac{1}{2})^0 \\ y=4\times1 \\ y=4 \end{gathered}$

For x = 1, we have

$\begin{gathered} y=4(\frac{1}{2})^x \\ y=4(\frac{1}{2})^1 \\ y=4\times\frac{1}{2} \\ y=2 \end{gathered}$

For x = 2, we have

$\begin{gathered} y=4(\frac{1}{2})^x \\ y=4(\frac{1}{2})^2 \\ y=4\times\frac{1}{4} \\ y=1 \end{gathered}$

Hence the table is

You can see from the table that as the value of x increases by 1 unit, the value of y decreases by 1/2. So, this is an exponential function.