Write down the amount of electrical charge in the battery at $t = 0$.

The line $L$ is the horizontal asymptote to the graph.

Write down the equation of $L$.

To download a game to the mobile phone, an electrical charge of 2.4 units is needed.

Find the time taken to reach this charge. Give your answer correct to the nearest minute.

$1.5$     (A1)     (C1)

[1 mark]

$C = 2.5$   (accept $y = 2.5$)     (A1)(A1)     (C2)

Notes: Award (A1) for $C{\text{ (or }}y) =$ a positive constant, (A1) for the constant $= 2.5$.

     Answer must be an equation.

[2 marks]

$2.4 = 2.5 - {2^{ - t}}$     (M1)

Note: Award (M1) for setting the equation equal to 2.4 or for a horizontal line drawn at approximately $C = 2.4$.

     Allow $x$ instead of $t$.

OR

$- t\ln (2) = \ln (0.1)$     (M1)

$t = 3.32192 \ldots$     (A1)

$t = 3{\text{ hours and 19 minutes (199 minutes)}}$     (A1)(ft)     (C3)

Note: Award the final (A1)(ft) for correct conversion of their time in hours to the nearest minute.

[3 marks]