# The table below represents an exponential function. Construct that function and then identify the...

## Question:

The table below represents an exponential function. Construct that function and then identify the corresponding growth or decay rate in percentage form.

{eq}\begin{array}{ll} x & y \\ \hline 0 & 200 \\ 1 & 220\\ 2 & 242 \\ 3 & 266.2\\ \hline \end{array} {/eq}

## Creating Exponential Functions from Coordinate Points

Recall that the standard form of an exponential function is $$f(x) = ab^x$$

How might we generate such an equation if we are only given coordinate points that lie on the graph? Well there are two scenarios to consider.

Case 1: One of the points we have been given is of the form {eq}(0,d) {/eq}.

• In this case {eq}d {/eq} is our initial value in the equation and thus the leading coefficient {eq}a {/eq}.
• Set up the equation of the form {eq}f(x) = ab^x {/eq}, using any other coordinate point as well as the value for {eq}a {/eq}.
• Solve for {eq}b {/eq}.

Case 2: None of the points are of the form {eq}(0,d) {/eq}.

• In this case, use any two coordinate points and set up two equations of the form {eq}f(x) = ab^x {/eq} using your {eq}x {/eq} and {eq}y {/eq} values. That is use one coordinate point for each equation.
• Solve the resulting system of equations for {eq}a {/eq} and {eq}b {/eq}.