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
Added by Scanty M.
Step 1
The pollutant decays at a rate of 8% a day, so the decay term is -0.08P. Show more…
Show all steps
Close
Your feedback will help us improve your experience
James Kiss and 58 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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.
Mathematical Modeling using Differential Equations
Mathematical Modeling: Setting up a Differential Equation
A radioactive substance has a decay constant equal to $4.4 \times 10^{-8} \mathrm{s}^{-1} .$ What is the half-life of this substance?
Substance $A$ decomposes at a rate proportional to the amount of A present. a) Write an equation relating $A$ to the amount left of an initial amount $A_{0}$ after time $t$ b) It is found that 8 g of $A$ will reduce to $4 \mathrm{g}$ in $3 \mathrm{hr}$. After how long will there be only 1 g left?
Exponential and Logarithmic Functions
Applications: Decay
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD