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2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), t = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area 4 of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.

2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), t = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area 4 of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), 1 = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area A of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.
Transcribed Image Text:2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), 1 = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area A of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.
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