5. A corporation maintains a balance of B(t) (in millions of dollars) in an account, where t is measuredin years. Interest with a nominal annual rate of 2% compounds continuously (that is, the rate atwhich interest is added to the account is proportional to B with proportionality constant 0.02year ¹). In addition, the corporation continuously withdraws money from the account at a rate of4 million dollars per year.(a) Write a differential equation for the balance B(t).(b) Find all solutions to your differential equation.(c) Suppose that B(0) = 300. Determine lim B(t) and interpret your result.t→∞(d) Suppose instead that B(0) = 100. When will the account be empty?

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Answered: 5. A corporation maintains a balance of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

According to Newton’s Law of Cooling, the rate of change of the temperature of an objectcan be modeled using the following differential equation: dT/dt=−κ(T−A) where T is the temperature of the object (in◦F), A is the room temperature (in◦F), and κ is the constant of proportionality. (a) Use an appropriate method to solve the differential equation.Remember that κ and A are constants. (b) Use your answer to (a) to solve the following: On a crime show, a dead body is discovered in a hotel room. A forensic technician recordedthat the victim’s body temperature was 91.4◦F at 6:00 pm. One hour later, the coroner arrived and found that the victim’s body temperature had fallen to 88.7◦F. If the thermostatin the hotel room is set at 68◦F, determine when the victim was murdered.(Assume the victim was a healthy 98.6◦F at the time of death.)
1. A population grows continuously at the rate of 8% per year. How long does it take for the population to double ? Use differential equation it.
A fish hatchery has 500 fish at time ? = 0. Each year 40 fish are harvested (evenly, throughoutthe year). The population’s instantaneous growth rate is 10% per year. Thus after 1 year, if nofish were harvested, there would be slightly more than 550 fish. a) Create the modeling differential equation for the amount of the number of fish in the hatchery, y, at time t.b) Solve the differential equation.c) Is there a steady-state level of the number of fish in the hatchery?
A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?
The air in a crowded room full of people contains .25% carbon dioxide (CO2). An air conditioner is turned on that blows fresh air into the room at the rate of 500 cubic feet per minute. The fresh air mixes with the stale air, and the mixture leaves the room at the rate of 500 cubic feet per minute. The fresh air contains .01% CO2, and the room has a volume of 2500 cubic feet. (a) Find a differential equation satisfied by the amount f(t)of CO2 in the room at time t.(b) The model developed in part (a) ignores the CO2 produced by the respiration of the people in the room. Suppose that the people generate .08 cubic foot of CO2 per minute. Modify the differential equation in part (a) totake into account this additional source of CO2.

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