Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
### Approximate the Change in Atmospheric Pressure with Increase in Altitude **Problem Statement:** Approximate the change in the atmospheric pressure when the altitude increases from \( z = 9 \) km to \( z = 9.05 \) km using the formula: \[ P(z) = 1000 e^{-\frac{z}{10}} \] **Instructions to Solve:** 1. **Understand the Formula:** The given formula \( P(z) = 1000 e^{-\frac{z}{10}} \) represents the atmospheric pressure at a certain altitude \( z \) (in kilometers). 2. **Evaluate the Pressure at Different Altitudes:** - Compute \( P(z) \) at \( z = 9 \) km. - Compute \( P(z) \) at \( z = 9.05 \) km. 3. **Compute the Change:** Subtract the pressure at \( z = 9.05 \) km from the pressure at \( z = 9 \) km to approximate the change in atmospheric pressure. **Interactive Component:** __Enter your answer in the answer box below:__ \[ \text{From } z = 9 \text{ km to } z = 9.05 \text{ km, the change in atmospheric pressure is approximately } \boxed{\phantom{answer}} \] (Type an exact answer.) --- **Note:** The visual depicted is a screenshot from a computer screen displaying the task described. There are no graphs or diagrams in the image to explain further.
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Transcribed Image Text:### Approximate the Change in Atmospheric Pressure with Increase in Altitude **Problem Statement:** Approximate the change in the atmospheric pressure when the altitude increases from \( z = 9 \) km to \( z = 9.05 \) km using the formula: \[ P(z) = 1000 e^{-\frac{z}{10}} \] **Instructions to Solve:** 1. **Understand the Formula:** The given formula \( P(z) = 1000 e^{-\frac{z}{10}} \) represents the atmospheric pressure at a certain altitude \( z \) (in kilometers). 2. **Evaluate the Pressure at Different Altitudes:** - Compute \( P(z) \) at \( z = 9 \) km. - Compute \( P(z) \) at \( z = 9.05 \) km. 3. **Compute the Change:** Subtract the pressure at \( z = 9.05 \) km from the pressure at \( z = 9 \) km to approximate the change in atmospheric pressure. **Interactive Component:** __Enter your answer in the answer box below:__ \[ \text{From } z = 9 \text{ km to } z = 9.05 \text{ km, the change in atmospheric pressure is approximately } \boxed{\phantom{answer}} \] (Type an exact answer.) --- **Note:** The visual depicted is a screenshot from a computer screen displaying the task described. There are no graphs or diagrams in the image to explain further.
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