Question

A pollutant spilled on the ground decays at a rate of $8 \%$ a day. In addition, cleanup crews remove the pollutant at a rate of 30 gallons a day. Write a differential equation for the amount of pollutant, $P$, in gallons, left after $t$ days.

Name: Problem 7, Chapter 9: Applied Calculus
Uploaded: 2020-05-13T21:27:01-08:00
Duration: 2 min
Channel: Zach Wiebe
Description: A pollutant spilled on the ground decays at a rate of 8 % a day. In addition, cleanup crews remove the pollutant at a rate of 30 gallons a day. Write a differential equation for the amount of pollutant, P, in gallons, left after t days.

   A pollutant spilled on the ground decays at a rate of $8 \%$ a day. In addition, cleanup crews remove the pollutant at a rate of 30 gallons a day. Write a differential equation for the amount of pollutant, $P$, in gallons, left after $t$ days.

Applied Calculus

Deborah… 5th Edition

Chapter 9, Problem 7

Instant Answer

Solved by Expert Zach Wiebe

05/13/2020

Step 1

This means that the amount of pollutant decreases by 8% of its current amount each day. In terms of a differential equation, this can be represented as $-0.08P$, where $P$ is the amount of pollutant. Show more…

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A pollutant spilled on the ground decays at a rate of $8 \%$ a day. In addition, cleanup crews remove the pollutant at a rate of 30 gallons a day. Write a differential equation for the amount of pollutant, $P$, in gallons, left after $t$ days.

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Key Concepts

Differential Equations

Differential equations are mathematical formulations that relate a function to its rate of change, allowing us to model dynamic systems where variables evolve continuously over time.

Exponential Decay

Exponential decay describes a process where the rate of decrease of a quantity is directly proportional to its current value, leading to a rapid reduction that slows over time. It is used to model natural decay processes in various fields.

Constant Rate Removal

Constant rate removal refers to the continuous extraction or loss of a quantity at a fixed amount per unit time, independent of the current level of that quantity. This concept is important in applied problems where an external process removes or adds a constant quantity to the system.

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