W523 (Section 6.2) Name: 1. The rate of change of the income produced by a vending machine is given by f(t) = 5,000e0 04 where t is the time in years since the installation of the machine. Find the total income produced (to the nearest dollar) during the first 5 years of operation 2. Using the continuous income rate of flow for the vending machine f(t) = 5,000e0.0+, find the future value of this income stream at 9%, compounded continuously for 5 years. 3. Starting at age 35, you deposit $3000 a year into an IRA account for retirement. Treat the yearly deposits into the account as a continuous income stream. If money in the account earns 5%, compounded continuously, how much will be in the account 30 years later, when you retire at age 65