The rate of decay of the mass is modelled by the differential equation dx/dt = -(5/2)x. Given that x = 60 when t = 0, solve the quation for x in terms of t.

(1) Rearrange the equation so that the left hand side is a function of x, and the right hand side is a function of t only.dx/dt = - (5/2) x(1/x)dx = -(5/2)dt(2) Integrate both sidesln(x/A) = -(5/2)t, where A is the integration constant, chosen to be lnA with no loss of generality(3) Rearrange for xx/A = exp(-(5/2)t)x = Aexp(-(5/2)t)(4) Use the boundary condition that x=60 when t=0.60 = A * 1A = 60x = 60exp(-(5/2)t)