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- [Instructor] Let of y of t represent your retirement account balance in dollars after t years. Each year the account earns 5% interest, and were assuming 5% continuous interest, and you deposit 8% of your annual income. Your current annual income is $50,000, but it is growing at a continuous rate of 4% per year. Were asked to write the differential equation modeling this situation. Well, the differential equation will be: the change in the balance with respect to time equals the change in the balance from interest with respect to time plus the change in the balance from the deposits with respect to time. Before we set this up, lets review the equation we use for continuous interest. If an account is paying continuous interest, then the account balance, y of t, equals P times e raised to the power of r t, where y of t is the account balance after t years, P is the principal or starting amount, r is the continuous growth rate per year, and t is time in years. Now, if we consider the