Drawing Growth
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 3 of 49.
Two points pin down an exponential, and y = a × b^x hands you both. At x = 0 the power is 1, so the output is a. At x = 1 the power is b, so the output is a times b.
Take y = 4 × 2^x. At x = 0 the output is 4, which gives the point (0, 4). At x = 1 it is 4 × 2, which is 8, so the second point is (1, 8). One more step gives (2, 16): each step right doubles the height, and the curve bends upward faster and faster.
It works the other way too: from two such points, the first height is a, and the second height divided by the first is b. From (0, 4) and (1, 8), a is 4 and b is 8 over 4, which is 2.
Challenge
Draw the graph of y = 2 × 3^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