Growing by a Percent

Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 5 of 46.

A jacket costs 100 dollars. The price drops 50%, to 50 dollars. Then it goes up 50%, to 75 dollars. It does not come back to 100.

Going up by a percent r means multiplying by $1+r$ . Going down means multiplying by $1-r$ . Here $0.5\cdot 1.5 = 0.75$ .

The same percent again and again gives exponential growth. 5000 dollars at 4% a year is $5000\cdot {1.04}^{t}$ after t years.

Challenge

A car worth 5000 dollars loses 20% of its value each year. Find its value V after 3 years. On the first line, write $V = ...$ 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 Growth Doubling Drawing 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 PercentHow 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