## Constructing and Comparing Linear and Exponential Models

In biology, students must grow and compare the height of two different plants over the period of a week. Plant one started as a seed and grew one inch every day. Plant two started at half an inch and doubled in height every day. Write and compare sequences for the two plants.

**Plant one: 0, 1, 2, 3, 4, 5, 6, 7**

**Plant two: .5, 1, 2, 4, 8, 16, 32**

Using this information, we can easily see that each plant does not increase in the same way each day. Plant one simply grows an inch each day, while plant two doubles it's previous height each day. With this, we can see that plant one represents a linear function and plant two is exponential.

Plant one has a constant percent rate of +1, while plant two has a constant rate of 2. Plant one is increasing at a constant rate, making it linear, while plant two doubles each day, making it exponential.

Plant one has a constant percent rate of +1, while plant two has a constant rate of 2. Plant one is increasing at a constant rate, making it linear, while plant two doubles each day, making it exponential.