1.6 Differentiation

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Question 32

The mass, $M$ kg, of a block of dry ice as it sublimates in a controlled environment $t$ hours after the start of an experiment is modelled by the equation

M = 12 + Pe^{-kt}

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

Given that the mass of the block at the start of the experiment was $40$ kg,

find the value of $P$ .

[1]

Given also that, exactly 5 hours after the start of the experiment, the mass of the block was $25$ kg,

find the value of $k$ to 3 significant figures.

[3]

Using the values for $P$ and $k$ ,

find, according to the model, the rate of change of the mass of the block exactly 8 hours after the experiment started. Give your answer in $h−1\text{kg}\text{ h}^{-1}$ to 3 significant figures.

[3]

Explain why, according to the model, the mass of the block cannot fall to $10$ kg.

[1]

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation

A Level
Maths CCEA
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