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1. Set up and solve a differential equation that models the following situation: An aquarium holds 5000 gallons of water. It is maintained with a pumping system that pumps in 100 gallons of water per minute. Water is drained from the aquarium at the same rate. (Water is not recycled.) An antibiotic is introduced into the inflow system, with a concentration of 10te-/50 milligrams per gallon, where t is measured in minutes. Assume the concentration of the antibiotic is uniform throughout the tank (it is mixed instantly). (a) Set up a differential equation (initial value problem) that models the amount of of antibiotic in the tank, as a function of time. Be sure to define variables, and state the units for each the variables. (b) Solve the initial value problem. Show all of the steps you took to solve the initial value problem. (c) When does the maximum concentration of antibiotic occur, and what is the maximum con- centration? Show your work, and include units in your answer.

1. Set up and solve a differential equation that models the following situation: An aquarium holds 5000 gallons of water. It is maintained with a pumping system that pumps in 100 gallons of water per minute. Water is drained from the aquarium at the same rate. (Water is not recycled.) An antibiotic is introduced into the inflow system, with a concentration of 10te-/50 milligrams per gallon, where t is measured in minutes. Assume the concentration of the antibiotic is uniform throughout the tank (it is mixed instantly). (a) Set up a differential equation (initial value problem) that models the amount of of antibiotic in the tank, as a function of time. Be sure to define variables, and state the units for each the variables. (b) Solve the initial value problem. Show all of the steps you took to solve the initial value problem. (c) When does the maximum concentration of antibiotic occur, and what is the maximum con- centration? Show your work, and include units in your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Set up and solve a differential equation that models the following situation: An aquarium holds 5000 gallons of water. It is maintained with a pumping system that pumps in 100 gallons of water per minute. Water is drained from the aquarium at the same rate. (Water is not recycled.) An antibiotic is introduced into the inflow system, with a concentration of 10te-t/50 milligrams per gallon, where t is measured in minutes. Assume the concentration is uniform throughout the tank (it is mixed instantly). the antibiotic (a) Set up a differential equation (initial value problem) that models the amount of of antibiotic in the tank, as a function of time. Be sure to define variables, and state the units for each the variables. (b) Solve the initial value problem. Show all of the steps you took to solve the initial value problem. (c) When does the maximum concentration of antibiotic occur, and what is the maximum con- centration? Show your work, and include units in your answer.
Transcribed Image Text:1. Set up and solve a differential equation that models the following situation: An aquarium holds 5000 gallons of water. It is maintained with a pumping system that pumps in 100 gallons of water per minute. Water is drained from the aquarium at the same rate. (Water is not recycled.) An antibiotic is introduced into the inflow system, with a concentration of 10te-t/50 milligrams per gallon, where t is measured in minutes. Assume the concentration is uniform throughout the tank (it is mixed instantly). the antibiotic (a) Set up a differential equation (initial value problem) that models the amount of of antibiotic in the tank, as a function of time. Be sure to define variables, and state the units for each the variables. (b) Solve the initial value problem. Show all of the steps you took to solve the initial value problem. (c) When does the maximum concentration of antibiotic occur, and what is the maximum con- centration? Show your work, and include units in your answer.
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