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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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? 

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Step 1: Rewrite given info:

To find the time at which the ground is completely free of snow, we need to solve for t when h(t) becomes zero. We have the differential equation:

fraction numerator d h over denominator d t end fraction space equals space 3 over 5 space minus space 9 over 20 h the  initial condition h( 0)=4.


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