Question

Write the exponential function for the data displayed in the following table

Answer 1

As per given by the question,

There are given that a table of x and f(x).

Now,

The genral for of the equation is,

`f(x)=ab^x`

Then,

For the value of x and f(x).

Substitute 0 for x and -2 for f(x).

So,

`\begin{gathered} f(x)=ab^x \\ -2=ab^0 \\ -2=a \end{gathered}`

Now,

For the value of b,

Substitute 1 for x and -1/3 for f(x),

So,

`\begin{gathered} f(x)=ab^x \\ -(1)/(3)=ab^1 \\ ab=-(1)/(3) \end{gathered}`

Now,

Put the value of a in above result.

So,

`\begin{gathered} ab=-(1)/(3) \\ -2b=-(1)/(3) \\ b=(1)/(6) \end{gathered}`

Now,

Put the value of a and b in the general form of f(x).

`\begin{gathered} f(x)=ab^x \\ f(x)=-2\cdot((1)/(6))^x \end{gathered}`

Hence, the exponential function is ,

`f(x)=-2((1)/(6))^x`