Applications of Recurrence Relations
Interactive practice questions
A cake is taken out of a $156^\circ$156°C oven and left to cool in a room with a constant temperature of $26^\circ$26°C.
As soon as it is taken out, the temperature of the cake drops by $2.5^\circ$2.5°C each minute.
What is the temperature of the cake after $8$8 minutes?
Write a recurrence relation that gives the temperature $T_n$Tn of the cake after $n$n minutes in terms of $T_{n-1}$Tn−1.
By how many degrees has the temperature of the cake dropped after half an hour?
Find the number of minutes it will take for the cake to reach room temperature.
For a photo, the staff at a company have been arranged such that there are $9$9 people in the front row and each row has $2$2 more people than in the row in front of it.
A basketball is dropped onto the ground from a height of $15$15 feet.
On each bounce, the ball reaches a maximum height of $55%$55% of its previous maximum height.
Farhan has saved up $\$2540$$2540 to spend during his holiday to Lebanon. He plans to spend $\$310$$310 each week while he is there.
Let $t_n$tn be the amount of savings Farhan has left at the beginning of week $n$n.