The rate of biomass accumulation in a soil sample, BBB (measured in mg per day), is modeled as a function of the nitrogen concentration nnn (in parts per million) by the equation:
B(n)=5n−3n2−n,n>1 B(n) = \frac{5n - 3}{n^2 - n}, \quad n > 1 B(n)=n2−n5n−3,n>1Express B(n)B(n)B(n) in partial fractions.
Hence find ∫B(n) dn\displaystyle \int B(n) \, dn∫B(n)dn.
Use your answer to part (b) to find the value of kkk for which the total biomass accumulation between concentration levels n=kn = kn=k and n=2kn = 2kn=2k is exactly ln72\ln 72ln72, where k>1k > 1k>1.
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