Graphs of Exponential Functions Examples

Is the following graph exponential growth or decay?

This is an exponential growth graph. Reading the graph left to right, notice the y values increase and the horizontal asymptote starts at the left of the graph. It would be exponential decay if the horizontal asymptote was at the right of the graph. Don't you feel smart now?

Is the graph below exponential growth or decay?

One might think this was exponential decay due to the severe plunge of the y values. Remember the rule: asymptote on the left = growth, asymptote on the right = decay. The function is decreasing exponentially making it exponential growth.

What equation goes with which graph? y = 3(80)^x and y = 3(1.8)^x?

The purple graph goes with the y = 3(80)^x and the green graph goes with y = 3(1.8)^x. Why? Think about it. Plug in an x value to either equation and you can see that 80^x will be a much higher number than 1.8^x. So the general rule is that the y = ab^x b value will be a much sharper curve, the higher the number.

What equation goes with which graph? y = -3(2)^x and y = 3(2)^x?

This one is pretty straight forward. They both have a horizontal asymptote of y = 0. They both are exponential growth equations.

The negative number for the a value tells us concavity in exponential functions. Since the red graph is concave up, the equation for that is y = 3(2)^x. The orange graph is concave down, so it's equation is y = -3(2)^x.

One way to verify that is to choose an x value and plug it into each equation to see what the y value is. Plug it in, plug it in.