Growing by a Percent
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 8 of 49.
You put 5000 dollars in an account that pays 4% a year. After one year you have the 5000 plus 4% of it: 5000 + 0.04 × 5000. That is 5000 × (1 + 0.04), or 5000 × 1.04, which is 5200. Keeping all of it is the 1, and the growth is the 0.04.
The second year pays 4% of the new amount, 5200, so it multiplies by 1.04 again. Two years give 5000 × 1.04^2, which is 5408. Growth by a percent is an exponential whose b is 1 plus the rate as a decimal.
Adding 4% of the original 5000 each year would give only 5400. The extra 8 dollars is interest earned on interest. It is small at first, and it is what makes long-term savings grow so much.
Challenge
You put 2000 dollars in an account that grows by 10% a year. Find its value V after 2 years, in dollars. On the blank board, first write a V = ... line as the start times a power, then work out its value on the next line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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