Use the model to find the volume of the barrel.

The empty barrel is being filled with water. The volume $V{\text{ }}{{\text{m}}^3}$ of water in the barrel after $t$ minutes is given by $V = 0.8(1 - {{\text{e}}^{ - 0.1t}})$. How long will it take for the barrel to be half-full?

attempt to substitute correct limits or the function into the formula involving

${y^2}$

eg$\,\,\,\,\,$$\pi \int_{ - 0.5}^{0.5} {{y^2}{\text{d}}x,{\text{ }}\pi \int {{{( - 0.8{x^2} + 0.5)}^2}{\text{d}}x} }$

0.601091

volume $= 0.601{\text{ }}({{\text{m}}^3})$     A2     N3

[3 marks]

attempt to equate half their volume to $V$     (M1)

eg$\,\,\,\,\,$$0.30055 = 0.8(1 - {{\text{e}}^{ - 0.1t}})$, graph

4.71104

4.71 (minutes)     A2     N3

[3 marks]