1.6 Differentiation

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Question 22

The pressure, $P$ kPa, inside a vacuum chamber $t$ seconds after a suction pump is activated is modelled by the equation

P = 15 + Ae^{-kt}

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

Given that the pressure inside the chamber at the instant the pump was activated was $100$ kPa,

find the value of $A$ .

[2]

Given also that, exactly 15 seconds after the pump was activated, the pressure was $40$ kPa,

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

[4]

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

find, according to the model, the rate of change of the pressure inside the chamber exactly 5 seconds after the pump was activated. Give your answer in $s−1\text{kPa}\,\text{s}^{-1}$ to 3 significant figures.

[3]

Explain why, according to the model, the pressure cannot fall to $10$ kPa.

[2]

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation

A Level
Maths CCEA
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