Doubling
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 6 of 49.
A culture of 500 cells doubles every hour. After one hour there are 1000, after two 2000, after three 4000. Each hour multiplies by 2 once more, so after three hours the start has been multiplied by 2 × 2 × 2, which is 2^3. In one line: 500 × 2^3 = 4000.
That is an exponential with a = 500 and b = 2. After t doublings the amount is the start times 2^t. The exponent counts doublings, not hours: if the cells doubled every 2 hours instead, 6 hours would be only 3 doublings.
The common slip is multiplying by 2 times 3 instead of 2 to the 3. 500 × 6 is 3000, as if the cells had grown by the same amount each hour. Doubling grows by more each hour, because each hour doubles a bigger number.
Challenge
A colony of bacteria starts with 300 cells and doubles every hour. Find the number of cells P after 4 hours. On the blank board, first write a P = ... 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