**??? - 2013 JUNE Q11**

11. A hot drink when first made has a temperature which is 65°C higher than room temperature. The temperature difference,

(i) Show that 3 minutes after the drink is made,

ii) Write down an expression for the value of

(iii) Show that when

*d*°C, between the drink and its surroundings decreases by 1.7% each minute.(i) Show that 3 minutes after the drink is made,

*d*= 61.7 to 3 significant figures. [2]ii) Write down an expression for the value of

*d*at time*n*minutes after the drink is made, where*n*is an integer. [1](iii) Show that when

*d*< 3,*n*must satisfy the inequalityHence find the integer value of

iv) The temperature difference at any time

*n*for which*d*< 3 [4]iv) The temperature difference at any time

*t*minutes after the drink is made can also be expressed as*d*65 X 10^{-kt}, for some constant*k*. Use the value of*d*for 1 minute after the drink is made to calculate the value of*k*. Hence find the temperature difference 25.3 minutes after the drink is made [4]