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Repeated Multiplying

Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 1 of 46.

You can have a million dollars now, or 1 cent that doubles every day for 30 days. Take the cent. On day 30 it has doubled 29 times. That is ${2}^{29}$ cents, over 5 million dollars.

Multiplying by the same number at each step is called exponential growth. $y = a\cdot {b}^{x}$ starts at a. Each step multiplies by b.

Challenge

$f\left(x\right) = 3\cdot {2}^{x}$ starts at 3 and doubles at every step. Work out $f\left(5\right)$ , one line at a time. Work out the power first, then multiply.

Try it yourself

f\left(5\right)

Simplify

Given $f\left(x\right) = 3\cdot 2^{x}$

All lessons in Exponentials, Logs & Sequences

1Exponential Functions

Repeated MultiplyingDrawing 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 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