3.6 Integration (A-level only)

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Question 4

The mass $M$ grams of a crystal growing in a chemical bath at time $t$ hours is modelled by the differential equation

\frac{\text{d}M}{\text{d}t} = \frac{10t \sqrt{M}}{\text{e}^{2t}}, \quad M \ge 0, \quad t \ge 0

Given that the initial mass of the crystal is $4$ g, solve this differential equation to find an expression for $M12M^{\frac{1}{2}}$ in the form $M12=f(t)M^{\frac{1}{2}} = f(t)$ .

[6]

Hence determine the equation of the horizontal asymptote to the curve with equation $M12=f(t)M^{\frac{1}{2}} = f(t)$ .

[2]

The mass $M$ grams of a crystal growing in a chemical bath at time $t$ hours is modelled by the differential equation

\frac{\text{d}M}{\text{d}t} = \frac{10t \sqrt{M}}{\text{e}^{2t}}, \quad M \ge 0, \quad t \ge 0

Given that the initial mass of the crystal is $4$ g, solve this differential equation to find an expression for $M12M^{\frac{1}{2}}$ in the form $M12=f(t)M^{\frac{1}{2}} = f(t)$ .

Hence determine the equation of the horizontal asymptote to the curve with equation $M12=f(t)M^{\frac{1}{2}} = f(t)$ .

[2]

3.6 Integration (A-level only)

Question 4

Markscheme

3.6 Integration (A-level only)

Question 4

Markscheme

3.6 Integration (A-level only)

Question 4

3.6 Integration (A-level only) Questions

3.6 Integration (A-level only)

Question 4

3.6 Integration (A-level only) Questions