The mass of a biochemical sample MMM (measured in milligrams) varies over time ttt (measured in seconds, t>0t > 0t>0) according to a growth model. The mass-time curve passes through the point P(4,15)P(4, 15)P(4,15).
Given that
dMdt=5t2−402t \frac{\mathrm{d} M}{\mathrm{d} t} = \frac{5t^2 - 40}{2\sqrt{t}} dtdM=2t5t2−40Determine the equation of the tangent to the curve at the point PPP, writing your answer in the form M=kt+cM = kt + cM=kt+c, where kkk and ccc are integers to be found.
Find the function M(t)M(t)M(t).
