Drawing Decay
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 4 of 49.
A decay curve is drawn with the same two points. Take y = 9 × (1/3)^x. At x = 0 the height is a, which is 9, so the first point is (0, 9). At x = 1 the height is 9 × (1/3), which is 3, so the second point is (1, 3).
This time the second point is lower than the first. Each step right divides the height by 3: 9, then 3, then 1, then 1/3. The curve falls quickly at first and then flattens out, getting closer to the x-axis without touching it.
Reading back works as before: b is the second height divided by the first. From (0, 9) and (1, 3), b is 3 over 9, which is 1/3. A ratio below 1 is how you recognise decay on a graph.
Challenge
Draw the graph of y = 8 × (1/2)^x. Drag one handle to the point on the y-axis and the other to the point above x = 1.
Try it yourself
Draw the graph
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponentials, Logs & Sequences
1Exponential Functions
Repeated MultiplyingGrowth or DecayDrawing GrowthDrawing DecayRecap: Exponential Functions