Question

Find the equation of the exponential function represented by the table below:

Answer 1

`f(x)=5(4)^x`

Explanation:

The exponential function is
`f(x)=ab^x`.
`a` is the initial value of the function, or the y-value when x=0. In this case,
`a`=5. If we enter that into the equation:

`f(x)=5b^x`

Then we can use another point to solve for
`b`.

`20=5b^1`

Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.

`20=5b\\(20)/(5)=(5b)/(5)\\b=4`

Now that we have both the
`a` and
`b` value, we can return to the exponential function and fill in the blanks.

`f(x)=5(4)^x`

I hope this helps!