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 }*0.0625\text{ =}(1)/(2) \end{gathered}`

`\begin{gathered} \text{If x= 3 } \\ y=8(4)^(3-1) \\ y\text{ = 8 }*16\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)