Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
we are given this situation: snow is falling at a constant rate of 3/5 in per hour and is being removed at a constant rate of 45% of the amount of snow on the ground per hour. The height of snow as a function of time is h(t) where our initial condition is h(0)=4. Our differential equation would thus be dh/dt = 3/5 - (9/20)h. Solving this gives h(t)=4/3 + (8/3)e^(-(9/20)t). All of the snow cannot be removed under these conditions because we cannot solve for h(t)=0 because it is undefined. The lowest the snow can reach is about 4/3 inches. But how could we change the rate of snowfall and rate of snow removal so that h(t) could equal zero?

we are given this situation: snow is falling at a constant rate of 3/5 in per hour and is being removed at a constant rate of 45% of the amount of snow on the ground per hour. The height of snow as a function of time is h(t) where our initial condition is h(0)=4. Our differential equation would thus be dh/dt = 3/5 - (9/20)h. Solving this gives h(t)=4/3 + (8/3)e^(-(9/20)t). All of the snow cannot be removed under these conditions because we cannot solve for h(t)=0 because it is undefined. The lowest the snow can reach is about 4/3 inches. But how could we change the rate of snowfall and rate of snow removal so that h(t) could equal zero?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
See similar textbooks
icon
Related questions
Question
100%

we are given this situation: snow is falling at a constant rate of 3/5 in per hour and is being removed at a constant rate of 45% of the amount of snow on the ground per hour. The height of snow as a function of time is h(t) where our initial condition is h(0)=4. Our differential equation would thus be dh/dt = 3/5 - (9/20)h. Solving this gives h(t)=4/3 + (8/3)e^(-(9/20)t). All of the snow cannot be removed under these conditions because we cannot solve for h(t)=0 because it is undefined. The lowest the snow can reach is about 4/3 inches. But how could we change the rate of snowfall and rate of snow removal so that h(t) could equal zero? 

Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS