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Question 15

The temperature, $θ\theta$ (in $∘C^\circ\text{C}$ ), of a liquid chemical $t$ minutes after being placed in a cooling bath is modelled by the equation

\theta = 20 + B e^{-kt}

where $B$ and $k$ are positive constants.

Given that the initial temperature of the chemical is $85∘C85^\circ\text{C}$ , and that after 20 minutes its temperature is $48∘C48^\circ\text{C}$ :

Find the exact value of $k$ , writing your answer in the form $120ln⁡(pq)\frac{1}{20} \ln\left(\frac{p}{q} \right)$ where $p$ and $q$ are integers to be found.

[4]

Find the time taken for the temperature of the chemical to reach $30∘C30^\circ\text{C}$ . Give your answer to the nearest minute.

[3]

Find the rate of decrease of the temperature of the chemical when $t = 10$ . Give your answer in $∘C^\circ\text{C}$ per minute to 3 significant figures.

[3]

Markscheme

Practical applications Questions

A Level
Psychology
Practical applications

49 exam-style questions on OCR A Level Psychology Practical applications. Each one has a worked solution and a mark scheme showing where the marks go.

Practical applications

Question bank

Practical applications

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Question 15

The temperature, $θ\theta$ (in $∘C^\circ\text{C}$ ), of a liquid chemical $t$ minutes after being placed in a cooling bath is modelled by the equation

\theta = 20 + B e^{-kt}

where $B$ and $k$ are positive constants.

Given that the initial temperature of the chemical is $85∘C85^\circ\text{C}$ , and that after 20 minutes its temperature is $48∘C48^\circ\text{C}$ :

Find the exact value of $k$ , writing your answer in the form $120ln⁡(pq)\frac{1}{20} \ln\left(\frac{p}{q} \right)$ where $p$ and $q$ are integers to be found.

[4]

Find the time taken for the temperature of the chemical to reach $30∘C30^\circ\text{C}$ . Give your answer to the nearest minute.

[3]

Find the rate of decrease of the temperature of the chemical when $t = 10$ . Give your answer in $∘C^\circ\text{C}$ per minute to 3 significant figures.

[3]

Markscheme

Practical applications Questions

A Level
Psychology
Practical applications

49 exam-style questions on OCR A Level Psychology Practical applications. Each one has a worked solution and a mark scheme showing where the marks go.