The concentration $C\,$ of a catalyst in a chemical reaction vessel, measured in mg/L, is modelled by the equation

\frac{100}{5(3t - k)}, \quad t > \frac{k}{3}

where $t\,$ is the time in seconds since the start of the reaction, $k\,$ is a positive constant, and $\neq 3$ .

Find $dCdt\displaystyle \frac{dC}{dt}$ , giving your answer in simplest form in terms of $k$ .

The rate of change of the concentration at time $t = 1$ is -15 mg/L/s.

Find the two possible values of $k$ .

Given also that $k < 3$ ,

find the equation of the normal to the curve of $C\,$ against $t\,$ at the point where $t = 1$ , writing your answer in the form $a t + b C + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

Show, using algebraic integration, that

\int_{1}^{3} \frac{100}{5(3t - k)} \, dt = \lambda \ln 2

where $\lambda\,$ is a constant to be found.

The concentration $C\,$ of a catalyst in a chemical reaction vessel, measured in mg/L, is modelled by the equation

\frac{100}{5(3t - k)}, \quad t > \frac{k}{3}

where $t\,$ is the time in seconds since the start of the reaction, $k\,$ is a positive constant, and $\neq 3$ .

Find $dCdt\displaystyle \frac{dC}{dt}$ , giving your answer in simplest form in terms of $k$ .

The rate of change of the concentration at time $t = 1$ is -15 mg/L/s.

Find the two possible values of $k$ .

Given also that $k < 3$ ,

find the equation of the normal to the curve of $C\,$ against $t\,$ at the point where $t = 1$ , writing your answer in the form $a t + b C + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

Show, using algebraic integration, that

\int_{1}^{3} \frac{100}{5(3t - k)} \, dt = \lambda \ln 2

where $\lambda\,$ is a constant to be found.

11.2 Integrating f(ax + b)

Question 17

Markscheme

11.2 Integrating f(ax + b)

Question 17

Markscheme

11.2 Integrating f(ax + b)

Question 17

11.2 Integrating f(ax + b) Questions

11.2 Integrating f(ax + b)

Question 17

11.2 Integrating f(ax + b) Questions