4.6 Integration (A-level only)

A scientist is tracking the concentration of two specific catalysts in a chemical reaction chamber.

The concentration of the first catalyst, $C_1$ (in ppm), is modelled by the equation

C_1 = A e^{kt}, \quad t \ge 0

where $A\,$ and $k\,$ are positive constants and $t\,$ is the time in hours from the start of the reaction.

Given that:

the concentration of the first catalyst was 500 ppm at the start of the reaction
the concentration was 2500 ppm after 4 hours

Find the exact value of $A\,$ and the value of $k\,$ to 4 significant figures.

[4]

The concentration of the second catalyst, $C_2$ (in ppm), is modelled by the equation

C_2 = 50000 e^{-0.6t}, \quad t \ge 0

where $t\,$ is the time in hours from the start of the reaction.

Find the rate of decrease of the concentration of this second catalyst exactly 5 hours from the start. Give your answer to 3 significant figures.

[3]

At time $t = T$ , the concentrations of the two catalysts are equal.

Find the value of $T$ , giving your answer to 3 significant figures.

(Solutions relying entirely on calculator technology are not acceptable.)

[4]

4.6 Integration (A-level only)

A scientist is tracking the concentration of two specific catalysts in a chemical reaction chamber.

The concentration of the first catalyst, $C_1$ (in ppm), is modelled by the equation

C_1 = A e^{kt}, \quad t \ge 0

where $A\,$ and $k\,$ are positive constants and $t\,$ is the time in hours from the start of the reaction.

Given that:

the concentration of the first catalyst was 500 ppm at the start of the reaction
the concentration was 2500 ppm after 4 hours

Find the exact value of $A\,$ and the value of $k\,$ to 4 significant figures.

[4]

The concentration of the second catalyst, $C_2$ (in ppm), is modelled by the equation

C_2 = 50000 e^{-0.6t}, \quad t \ge 0

where $t\,$ is the time in hours from the start of the reaction.

Find the rate of decrease of the concentration of this second catalyst exactly 5 hours from the start. Give your answer to 3 significant figures.

[3]

At time $t = T$ , the concentrations of the two catalysts are equal.

Find the value of $T$ , giving your answer to 3 significant figures.

(Solutions relying entirely on calculator technology are not acceptable.)

[4]

4.6 Integration (A-level only)

4.6 Integration (A-level only) Questions