4. The table below shows the concentration of ozone in Earth's atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) 0 5 10 15 20 Ozone Units (y) 0.7 0.6 1.1 3.0 4.9
4. The table below shows the concentration of ozone in Earth's atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) 0 5 10 15 20 Ozone Units (y) 0.7 0.6 1.1 3.0 4.9
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.3: Rate Of Change And Slope
Problem 19PPS
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![### Concentration of Ozone in Earth's Atmosphere
The table below shows the concentration of ozone in Earth's atmosphere at different altitudes. The data demonstrates how ozone concentration varies with altitude, providing a basis for modeling using an exponential regression equation.
#### Data Table: Concentration of Ozone
| Altitude (x) | Ozone Units (y) |
|--------------|-----------------|
| 0 | 0.7 |
| 5 | 0.6 |
| 10 | 1.1 |
| 15 | 3.0 |
| 20 | 4.9 |
#### Objective
Using the data provided, we aim to write the exponential regression equation that models these data, rounding all values to the nearest thousandth.
#### Analysis
1. **Identify Data Points**: The table lists altitude (in units of x) and corresponding ozone units (in units of y).
2. **Exponential Regression**: Use the data points to calculate the exponential regression equation, which accurately represents the relationship between altitude and ozone concentration.
The goal is to find the equation in the form:
\[ y = a \cdot e^{bx} \]
where `a` and `b` are constants determined by regression analysis. This equation helps in predicting ozone concentration (y) at any given altitude (x). All values should be rounded to the nearest thousandth.
> Note: Solving for `a` and `b` involves computational steps including taking the natural logarithm of y-values and using least squares fitting, which might require the use of statistical software or a calculator capable of performing regression analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d622916-6deb-40d7-a5d6-6a8f38afa405%2F5d9d53f2-621a-49cd-8743-f3843a308e50%2Foagmd5t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Concentration of Ozone in Earth's Atmosphere
The table below shows the concentration of ozone in Earth's atmosphere at different altitudes. The data demonstrates how ozone concentration varies with altitude, providing a basis for modeling using an exponential regression equation.
#### Data Table: Concentration of Ozone
| Altitude (x) | Ozone Units (y) |
|--------------|-----------------|
| 0 | 0.7 |
| 5 | 0.6 |
| 10 | 1.1 |
| 15 | 3.0 |
| 20 | 4.9 |
#### Objective
Using the data provided, we aim to write the exponential regression equation that models these data, rounding all values to the nearest thousandth.
#### Analysis
1. **Identify Data Points**: The table lists altitude (in units of x) and corresponding ozone units (in units of y).
2. **Exponential Regression**: Use the data points to calculate the exponential regression equation, which accurately represents the relationship between altitude and ozone concentration.
The goal is to find the equation in the form:
\[ y = a \cdot e^{bx} \]
where `a` and `b` are constants determined by regression analysis. This equation helps in predicting ozone concentration (y) at any given altitude (x). All values should be rounded to the nearest thousandth.
> Note: Solving for `a` and `b` involves computational steps including taking the natural logarithm of y-values and using least squares fitting, which might require the use of statistical software or a calculator capable of performing regression analysis.
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