The rate of change of the temperature of a heated metal rod ( $T$ ) in a laboratory setting is directly proportional to the difference between the temperature of the rod and the constant room temperature ( $15∘C15^{\circ}\text{C}$ ).

Write down a differential equation for this relationship.

Show that $T = 15 + Ae^{kt}$ where $A\,$ and $k\,$ are constants.

Given that the initial temperature of the rod is $115∘C115^{\circ}\text{C}$ , write down the value of $A$ .

After 10 minutes, the temperature of the rod is $65∘C65^{\circ}\text{C}$ . Show that $k=−110ln⁡2\displaystyle k = -\frac{1}{10} \ln 2$ .

Write down a differential equation for this relationship.

Show that $T = 15 + Ae^{kt}$ where $A\,$ and $k\,$ are constants.

Given that the initial temperature of the rod is $115∘C115^{\circ}\text{C}$ , write down the value of $A$ .

After 10 minutes, the temperature of the rod is $65∘C65^{\circ}\text{C}$ . Show that $k=−110ln⁡2\displaystyle k = -\frac{1}{10} \ln 2$ .

4.6 Integration (A-level only)

Question 2

Markscheme

4.6 Integration (A-level only)

Question 2

Markscheme

4.6 Integration (A-level only)

Question 2

4.6 Integration (A-level only) Questions

4.6 Integration (A-level only)

Question 2

4.6 Integration (A-level only) Questions