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). My question is at what time would the ground be completely removed of snow (assuming it keeps snowing at our constant rate) if such is possible?

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). My question is at what time would the ground be completely removed of snow (assuming it keeps snowing at our constant rate) if such is possible?

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,...

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