The temperature, $\theta{}^\circ$C, of a cup of hot chocolate milk, as it cools to room temperatur

Question

The temperature, $\theta{}^\circ$C, of a cup of hot chocolate milk, as it cools to room temperature, can be modelled by the formula $\theta=27+qb^{-t}$, where $q$ and $b$ are constants and $t$ is the time of cooling in minutes. Measurements of $t$ and $\theta$ are shown in the table below. $t$$2$$4$$6$$8$$10$$12$ $\theta$$71$$59$$48$$43$$38$$35$ Explain how a straight line graph can be drawn to represent the formula and draw it for the given data.[4] Estimate the value of $q$ and of $b$.[3] Use your graph to estimate the temperature of the cup of tea when $t=7$[2] What is the room temperature? Explain how you obtain your answer.[2]

Accepted Answer

(a) Plot $\ln(\theta-27)$ against $t$: $y\approx4.12-0.171t$ (b) $q\approx61.8$, $b\approx0.842$ (c) $\theta\approx45.6^\circ\mathrm{C}$ (d) $27^\circ\mathrm{C}$

Linear Law - Predictions from Linearised Models

Linear Law - Predictions from Linearised Models

Solution:

Solution locked

\(t\)	2	4	6	8	10	12
\(\theta\)	71	59	48	43	38	35