Question

Find the equation of the expinential function represented by the table below

Answer 1

By definition, Exponential functions have the following form:

`y=ab^x^{}`

Where the variable "x" is the exponent, "a" is the initial value and "b" is the decay factor or the growth factor.

In this case, given the table shown in the exercise, you can find the value of "a" by identifying the output value for this input value:

`x=0`

You can identify that it is:

`y=a=0.2`

In order to find "b", you can divide an input value by the previous one. See the procedure below:

`\begin{gathered} (0.6)/(0.2)=3 \\ \\ (1.8)/(0.6)=3 \end{gathered}`

Therefore:

`b=3`

Knowing the values of "a" and "b", you can set up the following equation of the function:

`y=0.2(3)^x^{}`

The answer is:

`y=0.2(3)^x`