Repeated Multiplying
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 1 of 49.
A line adds the same amount at every step. An exponential function multiplies by the same amount instead. Take f(x) = 5 × 3^x. At x = 0 it gives 5, because 3^0 = 1. Each time x goes up by 1, the output is multiplied by 3 once more: 5, 15, 45, 135.
Compare the line g(x) = 5 + 3x, which starts at the same 5 and adds 3 each step: 5, 8, 11, 14. After three steps the line has reached 14 and the exponential 135. Multiplying pulls away from adding very fast, which is why money, populations and viruses are described with exponentials.
Every exponential has the shape y = a × b^x: a is the start, the output at x = 0, and b is the number you multiply by at each step. To evaluate one, work out the power first, then multiply by a: f(2) is 5 × 3^2, which is 5 × 9, or 45.
Challenge
Use f(x) = 3 × 2^x to work out f(4). Tap the move that uses the rule, then type the arithmetic line by line.
Try it yourself
Simplify the expression
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