**Understanding Drug Levels in the Bloodstream: An Analysis****Problem Description:**When a certain drug is taken orally, the concentration (in milligrams) of the drug in the bloodstream after $ t $ hours is shown in the accompanying graph. Your task is to find the average rate of change of the drug amount in the bloodstream during the time interval from 3 hours to 5 hours.**Graph Explanation:**The graph is labeled "Drug Levels in the Bloodstream" and depicts drug concentration over time. The x-axis represents time in hours, and the y-axis represents the amount of the drug in milligrams.- The curve on the graph starts at the origin, increases sharply, and then decreases after reaching a peak.- Two critical points are highlighted: - At $ t = 3 $ hours, the drug amount is 8.5 mg. - At $ t = 5 $ hours, the drug amount is 1.5 mg.A straight line connects these two points, representing the interval over which we calculate the average rate of change.**Calculation Task:**Determine the average rate of change in drug concentration from 3 to 5 hours. Formally, this is calculated as:\[\text{Average rate of change} = \frac{\text{Amount at } t = 5 \text{ hours} - \text{Amount at } t = 3 \text{ hours}}{5 - 3}\]Substitute the given values to find the solution.**Solution:**The average rate of change is ______ mg per hour.*Note: Use this framework to fill in the box with an integer or a decimal.*

Answered: Image /qna-images/answer/5774b68c-a7fc-4e84-8a5f-2ab6f05fcd14.jpg

When a certain drug is taken orally, the amount (in milligrams) of the drug in the bloodstream after t hours is shown in the graph. Find the average rate of change of the amount of the drug in the bloodstream during the time interval from 3 hr to 5 hr. Drug Levels in the Bloodstream 30- 25- 2 20- 15- 10- (3, 8.5) 5- (5, 1.5) 0- 0. Time (in hours) The average rate of change is (Type an integer or a decimal.) mg per hour. Amount (in mg) -3,

When a certain drug is taken orally, the amount (in milligrams) of the drug in the bloodstream after t hours is shown in the graph. Find the average rate of change of the amount of the drug in the bloodstream during the time interval from 3 hr to 5 hr. Drug Levels in the Bloodstream 30- 25- 2 20- 15- 10- (3, 8.5) 5- (5, 1.5) 0- 0. Time (in hours) The average rate of change is (Type an integer or a decimal.) mg per hour. Amount (in mg) -3,

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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Exponential Growth Model

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Question

**Understanding Drug Levels in the Bloodstream: An Analysis**

**Problem Description:**

When a certain drug is taken orally, the concentration (in milligrams) of the drug in the bloodstream after $ t $ hours is shown in the accompanying graph. Your task is to find the average rate of change of the drug amount in the bloodstream during the time interval from 3 hours to 5 hours.

**Graph Explanation:**

The graph is labeled "Drug Levels in the Bloodstream" and depicts drug concentration over time. The x-axis represents time in hours, and the y-axis represents the amount of the drug in milligrams.

- The curve on the graph starts at the origin, increases sharply, and then decreases after reaching a peak.
- Two critical points are highlighted:
- At $ t = 3 $ hours, the drug amount is 8.5 mg.
- At $ t = 5 $ hours, the drug amount is 1.5 mg.

A straight line connects these two points, representing the interval over which we calculate the average rate of change.

**Calculation Task:**

Determine the average rate of change in drug concentration from 3 to 5 hours.

Formally, this is calculated as:

\[
\text{Average rate of change} = \frac{\text{Amount at } t = 5 \text{ hours} - \text{Amount at } t = 3 \text{ hours}}{5 - 3}
\]

Substitute the given values to find the solution.

**Solution:**

The average rate of change is ______ mg per hour.

*Note: Use this framework to fill in the box with an integer or a decimal.*

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