Question

What is the equation for the Exponential Function below (you can use ^ to representexponential notation like you do on a calculator)

Answer 1

The general equation for the exponential equation is given as

$y=ar^{n-1}$$\begin{gathered} \text{where } \\ a\text{ = 8 } \\ \text{and } \\ r\text{ = 4} \\ n\text{ =x} \end{gathered}$

Substituting these values into the above equation yields

$y=8(4)^{x-1}$

Checking for x = -1 and x = 3, to find out if the values of y correspond with the one in the chart yields

$\begin{gathered} \text{If x=-1} \\ y=8(4)^{-1-1} \\ y=8(4)^{-2} \\ y\text{ = 8 }\times0.0625\text{ =}\frac{1}{2} \end{gathered}$

$\begin{gathered} \text{If x= 3 } \\ y=8(4)^{3-1} \\ y\text{ = 8 }\times16\text{ = 128} \end{gathered}$

Hence the equations hold since the values x and y are corresponding with those in the chart

$y=8(4)^{x-1}$

y = 8(4)^(x-1)