# Logarithms Lesson 2

### Justifying the Power Rule for Exponential Expressions

Josh and Arobindo write two equivalent exponential expressions that represent the growth of a magical beanstalk over several consecutive time periods of an undetermined length. In doing so, they justify a rule for rewriting exponential expressions of a certain form.

##### Episode 1: Making Sense

The students explore the growth of the beanstalk between Day 2 and Day 12. They mark in several mathematical relationships on a number line that represents this growth and write several exponential expressions.

##### Episode 2: Exploring

Josh and Arobindo explore the growth of the beanstalk between Day 5 and Day 19. They write two equivalent expressions to represent this growth and use a number line to justify their expressions.

##### Episode 3: Repeating Your Reasoning

The students represent the growth of the beanstalk over 101 2-day periods on a number line. They use their number line to justify two equivalent expressions that describe the growth over that period.

##### Episode 4: Repeating Your Reasoning

The students use a number line to explore the growth of the beanstalk over an unknown number of 1.5-day periods of time. They develop two equivalent exponential expressions to represent this growth.

##### Episode 5: Reflecting

Josh and Arobindo write a general equation that describes the equivalence of two exponential expressions.