The surface area $S$ (measured in $cm2\text{cm}^2$ ) of a particular fungus culture is observed over time $t$ (measured in hours). The growth of the culture is modeled by the differential equation

\frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0

Given that the initial surface area of the fungus is 9 cm² at $t = 0$ , solve this differential equation to find $S^{1/2}$ in terms of $t$ , giving your answer in the form $S^{1/2} = g(t)$ .

Hence find the equation of the horizontal asymptote to the curve with equation $S^{1/2} = g(t)$ .

The surface area $S$ (measured in $cm2\text{cm}^2$ ) of a particular fungus culture is observed over time $t$ (measured in hours). The growth of the culture is modeled by the differential equation

\frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0

Given that the initial surface area of the fungus is 9 cm² at $t = 0$ , solve this differential equation to find $S^{1/2}$ in terms of $t$ , giving your answer in the form $S^{1/2} = g(t)$ .

Hence find the equation of the horizontal asymptote to the curve with equation $S^{1/2} = g(t)$ .

3.6 Integration (A-level only)

Question 20

Markscheme

3.6 Integration (A-level only)

Question 20

Markscheme

3.6 Integration (A-level only)

Question 20

3.6 Integration (A-level only) Questions

3.6 Integration (A-level only)

Question 20

3.6 Integration (A-level only) Questions