The rate of biomass accumulation in a soil sample, $B$ (measured in mg per day), is modeled as a function of the nitrogen concentration $n$ (in parts per million) by the equation:

\frac{5n - 3}{n^2 - n}, \quad n > 1

Express $B (n)$ in partial fractions.

Hence find $dn\displaystyle \int B(n) \, dn$ .

Use your answer to part (b) to find the value of $k$ for which the total biomass accumulation between concentration levels $n = k$ and $n = 2 k$ is exactly $ln⁡72\ln 72$ , where $k > 1$ .

\int_k^{2k} B(n) \, dn = \ln 72

The rate of biomass accumulation in a soil sample, $B$ (measured in mg per day), is modeled as a function of the nitrogen concentration $n$ (in parts per million) by the equation:

\frac{5n - 3}{n^2 - n}, \quad n > 1

Express $B (n)$ in partial fractions.

Hence find $dn\displaystyle \int B(n) \, dn$ .

Use your answer to part (b) to find the value of $k$ for which the total biomass accumulation between concentration levels $n = k$ and $n = 2 k$ is exactly $ln⁡72\ln 72$ , where $k > 1$ .

\int_k^{2k} B(n) \, dn = \ln 72

1 Pure Mathematics

Question 221

Markscheme

1 Pure Mathematics

Question 221

Markscheme

1 Pure Mathematics

Question 221

1 Pure Mathematics Questions

1 Pure Mathematics

Question 221

1 Pure Mathematics Questions