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Doubling

Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 3 of 46.

500 cells double every hour. Many people say that after 3 hours there are $500\cdot 2\cdot 3$ , which is 3000. That is wrong. Each hour doubles a bigger number: 1000, then 2000, then 4000.

$500\cdot 2\cdot 2\cdot 2 = 500\cdot {2}^{3} = 4000$

The exponent, the small 3, counts the doublings, not the hours. If cells double every 2 hours, they double only 3 times in 6 hours.

Challenge

A group of 250 cells doubles every 2 hours. Find the number of cells P after 10 hours. On the first line, write $P = ...$ as the start times a power. On the second line, write its value.

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All lessons in Exponentials, Logs & Sequences

1Exponential Functions

Repeated Multiplying Drawing GrowthDoublingDrawing Decay

4Meet the Logarithm

What a Log Is Reading a Log Logs of Fractions From Log to Power Recap: Logarithms

7Log Equations

Combine, Then Undo A Difference of Logs Same Log Both Sides A False Answer Recap: Log Equations

10Final Challenges

Final: Same Base Final: Log It Final: Two Logs Final: The Investment Final: The Staircase

2Growth and Decay

Growing by a Percent How Long Until?Recap: Growth and Decay

5Log Rules

The Product Rule The Quotient Rule The Power Rule Into One Log Recap: Log Rules

8Arithmetic Sequences

The nth Term Which Term?Adding the Terms Recap: Arithmetic Sequences

3Same-Base Equations

Matching Powers Rewriting the Base An Expression Upstairs Fractions and Negatives Recap: Same Base

6Solving with Logs

Take the Log Isolate the Power First Base e Undoing ln Recap: Solving with Logs

9Geometric Sequences

Multiply Each Time Finding the Ratio Geometric Sums Forever Sums Recap: Geometric Sequences