6. A corporation maintains a balance of B(t) (in millions of dollars) in an account, where...

  

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6. A corporation maintains a balance of B(t) (in millions of dollars) in an account, where t is measured in years. Interest with a nominal annual rate of 2% compounds continuously (that is, the rate at which interest is added to the account is proportional to B with proportionality constant 0.02 year ¹). In addition, the corporation continuously withdraws money from the account at a rate of 4 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. (-400 (d) Suppose instead that B(0) 100. When will the account be empty? 6. A corporation maintains a balance of B(t) (in millions of dollars) in an account, where t is measured in years. Interest with a nominal annual rate of 2% compounds continuously (that is, the rate at which interest is added to the account is proportional to B with proportionality constant 0.02 year ¹). In addition, the corporation continuously withdraws money from the account at a rate of 4 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. (-400 (d) Suppose instead that B(0) 100. When will the account be empty?

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a Write a differential equation for the balance Bt The rate of change of the balance Bt with respect to time t is determined by the interest and the c... View the full answer