Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/ t and 72/ t approximations. In the SVG version, hover over a graph to highlight it …

To graph an exponential function, just plot its horizontal asymptote, its intercepts, and a few points on it. Learn the process of graphing exponential function along with many examples.

How the graph and equation of exponential decay functions relate. Practice problems with diagrams and examples.

In this unit, we learn how to construct, analyze, graph, and interpret basic exponential functions of the form f (x)=a⋅bˣ.

Think carefully about how you choose the scale for the axes. If you get stuck, consider creating a table of values. Use the graphing tool or technology outside the course. Graph the equation that …

Dec 1, 2025 · Graph y = (1 2) x and compare it to y = 2 x. Let’s make a table of both functions and then graph. Notice that y = (1 2) x is a reflection over the y -axis of y = 2 x. Therefore, instead of …

Graphing exponential decay using a table of values is the goal of this lesson.

Dec 15, 2024 · Using mathematical notation: as x → ∞, then y → 0. The vertical intercept is the point (0, a) on the y-axis. There is no horizontal intercept because the function does not cross the x-axis. The …

We say that such systems exhibit exponential decay, rather than exponential growth. The model is nearly the same, except there is a negative sign in the exponent.