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7:36 myopenmath.com ■ll 5G 29 pose: • The vat contains 270 gallons of liquid, which never changes. • Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. • Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: d.S 65 580 271 dt 13 ♂ 580 S 54 ☑ (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that 11 ހ J. 65 S(t) = 2706 ✓ 2412 - 280e σ K.e-14t+ Ке 13 31320 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 ☑ 1501.6989900366 tablespoons

7:36 myopenmath.com ■ll 5G 29 pose: • The vat contains 270 gallons of liquid, which never changes. • Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. • Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: d.S 65 580 271 dt 13 ♂ 580 S 54 ☑ (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that 11 ހ J. 65 S(t) = 2706 ✓ 2412 - 280e σ K.e-14t+ Ке 13 31320 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 ☑ 1501.6989900366 tablespoons

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 11P
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7:36 myopenmath.com ■ll 5G 29 pose: • The vat contains 270 gallons of liquid, which never changes. • Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. • Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: d.S 65 580 271 dt 13 ♂ 580 S 54 ☑ (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that 11 ހ J. 65 S(t) = 2706 ✓ 2412 - 280e σ K.e-14t+ Ке 13 31320 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 ☑ 1501.6989900366 tablespoons
Transcribed Image Text:7:36 myopenmath.com ■ll 5G 29 pose: • The vat contains 270 gallons of liquid, which never changes. • Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. • Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: d.S 65 580 271 dt 13 ♂ 580 S 54 ☑ (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that 11 ހ J. 65 S(t) = 2706 ✓ 2412 - 280e σ K.e-14t+ Ке 13 31320 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 ☑ 1501.6989900366 tablespoons
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