Lugo invests $1000 into an account that accumulates interest continuously with a force of interest δ(t) = 0.3 + 0.1t, where t measures the time in years, for 10 years. Celine invests $1000, also for 10 years, into a savings account that earns interest under a nominal annual interest rate of 12% compounded monthly. What is the difference amount between the amounts accumulated in Lugo’s and Celine’s accounts at the end of 10 years? (please show all work step by step in the problem)