**Stalactite Growth Data Analysis**The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the year 2000. The data through 2016 is shown below, where \( t \) is in years after the beginning of the year 2000.| \( t \) (years) | Length (mm) ||----------------|-------------|| 0 | 105 || 4 | 110 || 8 | 116 || 12 | 120 || 16 | 125 |**Tasks**1) **Pattern Identification** Use the data to construct a scatter plot. Then, choose which of the following best describes the pattern: - **A. Logistic** \[ y = \frac{c}{1 + a e^{-bx}} \] - **B. Exponential** \[ y = a \cdot b^x \] - **C. Linear** \[ y = mx + b \]2) **Model Calculation** Using your calculator and the best-fitting method from above, find a model, \( L(t) \), that estimates the length of the stalactite \( t \) years after 2000. **Round to two decimal places.** \( L(t) = \) [ ]3) **Analysis** Use your rounded answer from part 2 to complete the following. **Round to two decimal places.** According to the model, at the beginning of the year 2007: - The stalactite was approximately [ ] mm long. - It was growing at a rate of approximately [ ] mm per year.

We have to find part 1,2 and 3.

The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the year 2000. The data through 2016 is shown below, where t is in years after the beginning of the year 2000. t Length (mm) 0 105 Logistic y= (y= Use the data to construct a scatter plot, then complete the following. 1) Which of the following best describes the pattern? O A. C 1+ae - bx B. Exponential (y = a.bx) O C. Linear (y = mx + b) 4 110 8 116 2) Using your calculator and the best of the four methods above, find a model, L(t), that estimates the length of the stalactite t years after 2000. ROUND TO TWO DECIMAL PLACES. L(t) = 3) Use your rounded answer from part 2 to complete the following. ROUND TO TWO DECIMAL PLACES. Acording to the model, at the beginning of the year 2007, the stalactite was approximately mm long, and it was growing at a rate of approximately 12 120 mm per year. 16 125

The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the year 2000. The data through 2016 is shown below, where t is in years after the beginning of the year 2000. t Length (mm) 0 105 Logistic y= (y= Use the data to construct a scatter plot, then complete the following. 1) Which of the following best describes the pattern? O A. C 1+ae - bx B. Exponential (y = a.bx) O C. Linear (y = mx + b) 4 110 8 116 2) Using your calculator and the best of the four methods above, find a model, L(t), that estimates the length of the stalactite t years after 2000. ROUND TO TWO DECIMAL PLACES. L(t) = 3) Use your rounded answer from part 2 to complete the following. ROUND TO TWO DECIMAL PLACES. Acording to the model, at the beginning of the year 2007, the stalactite was approximately mm long, and it was growing at a rate of approximately 12 120 mm per year. 16 125

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

**Stalactite Growth Data Analysis**

The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the year 2000. The data through 2016 is shown below, where \( t \) is in years after the beginning of the year 2000.

| \( t \) (years) | Length (mm) |
|----------------|-------------|
| 0 | 105 |
| 4 | 110 |
| 8 | 116 |
| 12 | 120 |
| 16 | 125 |

**Tasks**

1) **Pattern Identification**

Use the data to construct a scatter plot. Then, choose which of the following best describes the pattern:

- **A. Logistic**
\[
y = \frac{c}{1 + a e^{-bx}}
\]

- **B. Exponential**
\[
y = a \cdot b^x
\]

- **C. Linear**
\[
y = mx + b
\]

2) **Model Calculation**

Using your calculator and the best-fitting method from above, find a model, \( L(t) \), that estimates the length of the stalactite \( t \) years after 2000. **Round to two decimal places.**

\( L(t) = \) [ ]

3) **Analysis**

Use your rounded answer from part 2 to complete the following. **Round to two decimal places.**

According to the model, at the beginning of the year 2007:
- The stalactite was approximately [ ] mm long.
- It was growing at a rate of approximately [ ] mm per year.

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