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5. A student opens a new savings account that continuously compounds interest at an annual rate 7'. She also (continuously) transfers money into this bank account at a rate of k dollars per year. Let V(t) denote the balance of the account and suppose Vb dollars are initially invested in the account. (a) Construct an IVP describing the way the balance in the student's bank account is changing. (b) Solve the IVP from part (a). (c) An important quantity in many differential equations is the doubling time. In this context, the doubling time is the length of time needed for the bank account to be double the student's initial investment. Find the doubling time, td, for this DE. ((1) Calculate the value of td if k = 0 and interpret this value in comparison to your solution from (c)