# Exponentials Lesson 4

### Exploring the Equations for Other Magical Beanstalks

The students explore the growth of new magical beanstalks. While all the beanstalks are similar in that they grow by a consistent factor each day, the factors they grow by are different and their heights on Day 0 are not always 1 cm. Josh and Arobindo explore how these changes affect the equations that model their growth.

##### Episode 1: Making Sense

The students use the timeline they made in the last lesson to determine the height of the beanstalk on Day 12.

##### Episode 2: Exploring

Arobindo and Josh create a timeline for a new magical beanstalk. This beanstalk’s height also increases by a factor of 3 each day, but it starts with a height of 2 cm on Day 0 instead of 1 cm. The students use their timeline to create an expression that represents the height of this new beanstalk on Day 12.

##### Episode 3: Repeating Your Reasoning

Josh and Arobindo use their new timeline to create an expression that represents the height of the new beanstalk on Day 100.

##### Episode 4: Repeating Your Reasoning

The students use their timeline to create an equation that gives the height of the new beanstalk on any day.

##### Episode 5: Reflecting

Josh and Arobindo are given an equation that models the growth of a magical beanstalk. They explain how the beanstalk is growing.

##### Episode 6: Reflecting

Arobindo and Josh are given equations that model the growth of magical beanstalks. They use these equations to compare and contrast how the beanstalks are growing.