The rate of change of the projected total assets (in constant 2005 dollars) in a government trust fund for the years 2000 through 2040 can be modeled as f(x)=0.365x2+0.294x+176.34 where output is measured in billion dollars per year and x is the number of years after 2000. Check: f(2)=174.292 (a) When will the trust fund assets be growing? When will they be declining? (Round your answers to the nearest integer.) The projected total assets in the trust fund are growing from the year :hrough the year X The projected total assets in the trust fund are declining from the year through the year (b) When will the amount in the trust fund be greatest? (Round your answer to three decimal places.) The amount in the trust fund will be at a maximum years after 2000. (c) Use a definite integral to find the total signed area between between f(x) and the x-axis from x=0 to x=29. (Round your answer to three decimal places.) Interpret the result. The amount in the trust fund is projected to grow by $ billion from the year 2000 to the year 2029