The temperature, $\theta^{\circ}\mathrm{C}$, of the water in a flask, $t$ minutes after the star

Question

The temperature, $\theta^{\circ}\mathrm{C}$, of the water in a flask, $t$ minutes after the start of heating is modelled by the equation $\theta = b + k \ln(2t + 1)$, where $b$ and $k$ are constants. Initially the temperature of the water is $20^{\circ}\mathrm{C}$. After $2$ minutes of heating, the temperature is $65^{\circ}\mathrm{C}$. Find the values of $b$ and $k$.[4] Find the time it takes for the water to reach a temperature of $50^{\circ}\mathrm{C}$.[3] Sketch the graph of the temperature of the water against time for $0 \le t \le 8$, labelling clearly the end points of the graph.[3] State, with a reason, whether this model is suitable in the long term.[2]

Accepted Answer

(i) $k= \frac{45}{\ln 5} $ (ii) $0.962 $ min

2016 RVHS H1 Promo Q11

2016 RVHS H1 Promo Q11