A synthetic crystal's mass growth rate, dmdt\displaystyle \frac{dm}{dt}dtdm in grams per hour, is modeled by the equation:
dmdt=15t3−45t,t>0 \frac{dm}{dt} = \frac{15t^3 - 4}{5\sqrt{t}}, \quad t > 0 dtdm=5t15t3−4,t>0where t t\,t is the time elapsed in hours. Determine the general expression for the mass m m\,m in terms of ttt, giving your answer in its simplest form.
