A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3000 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(0), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 26 years. (a) y' =O (Type an expression using y as the variable.) (b) () = D There will be s in the account at the end of 26 years. (Round to the nearest integer as needed.)

Suppose that P0 is invested in a savings account where interest is compounded continuously at 3.1% per year. A).Express P(t) in terms of Po where 0.031 is the rate. B).When will an investment of $1000 double itself ?

Suppose that P, is invested in a savings account in which interest is compounded continuously at 5.2% per year. That is, the balance P grows at the rate given by P = .052 P(t) dt a) Find the function P(t) that satisfies the equation. b) Suppose that $1200 is invested. What is the balance after 4 years? c) When will an investment of $1800 double itself?