??? - 2013 JUNE Q11
11. A hot drink when first made has a temperature which is 65°C higher than room temperature. The temperature difference, 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 inequality
(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 inequality
Hence find the integer value of 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]
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]