An amusement company maintains records for each video game it installs in an arcade. Suppose that C(t) and R(t) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed and the derivatives C'(t) and R'(t) are the functions below. C'(t) = 5 and R'(t) = 9 e -0.2t Find the area between the graphs of C' and R' over the interval on the t-axis from 0 to the useful life of the game and interpret the results. ..... What is the useful life of the game? t= years (Round to the nearest tenth as needed.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.