The concentration C in miligrams per milimeter (mg/ml) of a certain drug in a persons blood stream t hours after a pill is swallowed is modeled by C(t)=3+4t/1+t^3-e^-.001t. Estimate the change in concertration whe t changes from 30 to 40 minutes. The change in concentration is about blank mg/ml (type an integer or decimal rounded to the nearest thousandth as n
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
The concentration C in miligrams per milimeter (mg/ml) of a certain drug in a persons blood stream t hours after a pill is swallowed is modeled by C(t)=3+4t/1+t^3-e^-.001t. Estimate the change in concertration whe t changes from 30 to 40 minutes.
The change in concentration is about blank mg/ml
(type an integer or decimal rounded to the nearest thousandth as needed)
![**Educational Content: Drug Concentration Over Time**
The concentration \( C \) in milligrams per milliliter (\( \text{mg/ml} \)) of a certain drug in a person's bloodstream after a pill is swallowed is described by the function:
\[ C(t) = 3 + \frac{4t}{1 + t^3} - e^{-0.01t} \]
where \( t \) is the time in hours after the pill is swallowed.
**Objective:**
Estimate the change in concentration as \( t \) changes from 30 to 40 minutes.
**Instructions:**
- Calculate the concentration at \( t = 0.5 \) hours (30 minutes).
- Calculate the concentration at \( t = 0.6667 \) hours (40 minutes).
- Determine the change in concentration by finding the difference between these two values.
**Result:**
The change in concentration is about \(\_\_\_\) mg/ml.
(Type an integer or decimal rounded to the nearest thousandth as needed.)
**Interactive Component:**
- Enter your answer in the answer box and click "Check Answer."
![Graphical explanation is absent; provide numerical calculations based on concentration function.]*
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This guide is designed to help understand the process of calculating changes in drug concentration over a given timeframe using a mathematical model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fcbe7e9-6a87-442c-929e-82e9e6d1cd21%2Feb5ac995-aca0-4677-af6f-7302bb05b459%2F337zkqf_processed.jpeg&w=3840&q=75)
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