The rate of mass accumulation of a certain chemical product in a reaction, RRR in grams per minute, is modeled by the function
R(t)=10t−152t2−5t,t>2.5 R(t) = \frac{10t - 15}{2t^2 - 5t}, \quad t > 2.5 R(t)=2t2−5t10t−15,t>2.5where ttt is the time in minutes since the reaction began.
Express R(t)R(t)R(t) in partial fractions.
Hence find ∫R(t) dt\int R(t) \, dt∫R(t)dt.
Use your answer to part (b) to find the value of the constant kkk for which
∫k2kR(t) dt=ln72 \int_k^{2k} R(t) \, dt = \ln 72 ∫k2kR(t)dt=ln72
