Question

The rate of change of the level of ozone, an invisible gas that is an irritant and impairs breathing, present in the atmosphere on a certain May day in the city of Riverside is given by $$ R(t)=3.2922 t^{2}-0.366 t^{3} \quad(0<t<11) $$ (measured in pollutant standard index/hour). Here, $t$ is measured in hours, with $t=0$ corresponding to $7 \mathrm{a} . \mathrm{m}$. Find the ozone level $A(t)$ at any time $t$, assuming that at $7 \mathrm{a} \cdot \mathrm{m}$. it is zero.

Name: Problem 82, Chapter 11: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-08-01T00:08:35-08:00
Duration: 1 min 27 s
Channel: Lucas Finney

   The rate of change of the level of ozone, an invisible gas that is an irritant and impairs breathing, present in the atmosphere on a certain May day in the city of Riverside is given by
$$
R(t)=3.2922 t^{2}-0.366 t^{3} \quad(0<t<11)
$$
(measured in pollutant standard index/hour). Here, $t$ is measured in hours, with $t=0$ corresponding to $7 \mathrm{a} . \mathrm{m}$. Find the ozone level $A(t)$ at any time $t$, assuming that at $7 \mathrm{a} \cdot \mathrm{m}$. it is zero.

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 11, Problem 82

Instant Answer

Solved by Expert Lucas Finney

08/01/2021

Step 1

Since the rate of change is the derivative of the ozone level with respect to time, we can write this as: $$ R(t) = \frac{dA(t)}{dt} $$ Show more…

Show all steps

Thanks for your feedback!

The rate of change of the level of ozone, an invisible gas that is an irritant and impairs breathing, present in the atmosphere on a certain May day in the city of Riverside is given by $$ R(t)=3.2922 t^{2}-0.366 t^{3} \quad(0<t<11) $$ (measured in pollutant standard index/hour). Here, $t$ is measured in hours, with $t=0$ corresponding to $7 \mathrm{a} . \mathrm{m}$. Find the ozone level $A(t)$ at any time $t$, assuming that at $7 \mathrm{a} \cdot \mathrm{m}$. it is zero.

Play audio

Feedback

Lucas Finney and 98 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Initial Condition

An initial condition is a known value of the function at a specific point, which is used to determine the constant of integration when finding the antiderivative. In this setting, the initial ozone level at the starting time is provided, allowing for a complete and unique solution for the ozone level function.

Rate of Change

This concept refers to the measurement of how a quantity changes over time. In calculus, the rate of change is represented by the derivative of a function, which in this context is given by the ozone production rate. It provides the instantaneous change in the amount of ozone with respect to time.

Antiderivative

An antiderivative is the reverse process of differentiation, used to recover the original function from its derivative. When faced with a rate of change, the antiderivative (or indefinite integral) yields the total accumulated quantity, which in this problem represents the ozone level over time.

Please give Ace some feedback