Is TSI (y) a function of years (x)? How do you know this?
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Is TSI (y) a function of years (x)? How do you know this?
### TSI (trophic state index) of Lake Pamela
| x (Years since 2002) | y=f(x) TSI |
|----------------------|------------|
| 0 | 45.2 |
| 2 | 44.1 |
| 4 | 41.4 |
| 6 | 44.6 |
| 8 | 42.5 |
| 10 | 37.6 |
### TSI of Lake Pamela Graph
The graph represents the Trophic State Index (TSI) of Lake Pamela over years since 2002.
- **X-axis**: Represents the years since 2002, ranging from 0 to 12.
- **Y-axis**: Represents the TSI values, ranging from 0 to 80.
The plotted points on the graph show a general trend of decreasing TSI values, indicating an improvement in the lake's health over time. The TSI value is highest at 45.2 in the year 2002 and decreases to 37.6 by the year 2012, highlighting the effects of improved vegetation management practices around the lake.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6401d2b-4726-4617-af87-d155e639ffe3%2F851bcbad-2185-405d-9ac9-abe9b829f8b5%2Fzs5bia8.jpeg&w=3840&q=75)
Transcribed Image Text:# Linear Functions
## Modeling Real-Life Data
Lake Pamela is the large lake that you see on Valencia West Campus as you enter the school from Kirkman Road. From about 1996 to 2000, vegetation was taken out around the lakeshore to make it look more cosmetically pleasing. The water quality quickly declined due to increased nutrient flow into the lake, making the lake unhealthy. Around 2000, the vegetation removal and cutting of the grass down to the shoreline stopped, and more trees were planted. Lake Pamela's TSI (trophic state index) data is given in the table below (the maximum value for each year is used). The TSI of a lake measures the biological condition of the lake, or how healthy it is. Generally speaking, the lower the TSI, the healthier a lake is.
[Link to TSI information](http://www.hillsborough.wateratlas.usf.edu/shared/learnmore.asp?toolsection=lm_tsi)
### TSI (trophic state index) of Lake Pamela
| x (Years since 2002) | y=f(x) TSI |
|----------------------|------------|
| 0 | 45.2 |
| 2 | 44.1 |
| 4 | 41.4 |
| 6 | 44.6 |
| 8 | 42.5 |
| 10 | 37.6 |
### TSI of Lake Pamela Graph
The graph represents the Trophic State Index (TSI) of Lake Pamela over years since 2002.
- **X-axis**: Represents the years since 2002, ranging from 0 to 12.
- **Y-axis**: Represents the TSI values, ranging from 0 to 80.
The plotted points on the graph show a general trend of decreasing TSI values, indicating an improvement in the lake's health over time. The TSI value is highest at 45.2 in the year 2002 and decreases to 37.6 by the year 2012, highlighting the effects of improved vegetation management practices around the lake.
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