**?? - 2015 q4**

(a) Water is being heated in an electric kettle. The temperature, θ°C, of the water

θ = 120 - 100e

State the value of θ when

Given that the temperature of the water in the kettle is 70°C when t = 40,

b) find the exact value of λ, giving your answer in the form ln

When t = T, the temperature of the water reaches 100°C and the kettle switches off.

(c) Calculate the value of T to the nearest whole number. (2)

*t*seconds after the kettle is switched on, is modelled by the equation^{λt}, 0 ≤

*t*≤

*T*

State the value of θ when

*t*= 0 (1)Given that the temperature of the water in the kettle is 70°C when t = 40,

b) find the exact value of λ, giving your answer in the form ln

*a*/*b*, where*a*and*b*are integers (4)When t = T, the temperature of the water reaches 100°C and the kettle switches off.

(c) Calculate the value of T to the nearest whole number. (2)