Losing a Percent
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 9 of 49.
A phone worth 800 dollars loses 25% of its value each year. Losing 25% leaves 75%, so each year multiplies the value by 0.75, which is 1 minus 0.25. After one year it is worth 800 × 0.75, which is 600.
The second year takes 25% of 600, not of 800, so it multiplies by 0.75 again: 800 × 0.75^2, which is 450. The phone lost 200 dollars in the first year and only 150 in the second, because each year's loss is a share of a smaller value. That is decay with b equal to 1 minus the rate.
The common slip is multiplying by the 0.25 itself. That gives what was lost, not what is left. Ask what share remains, and multiply by that.
Challenge
A car worth 5000 dollars loses 20% of its value each 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