A-level · Exponentials & logarithms

Exponential growth and decay modelsExam-style questions

Real-world models of the form N = N0 e^{kt} (or A = a + b e^{kt}): finding the starting value, fitting the rate constant to data with logs, interpreting parameters, rates and limiting values.

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26 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A loaf of bread is taken out of an oven and left on a wire rack to cool.

A model for the core temperature of the loaf is

$\theta = A\,e^{-Bt} + 21$

where $\theta\ ^\circ$ C is the core temperature of the loaf $t$ minutes after it is taken out of the oven, and $A$ and $B$ are constants.

The loaf comes out of the oven with a core temperature of $96\ ^\circ$ C.
(a) State the value of $A$ .

(1 mark)

As the loaf comes out of the oven, its core temperature is falling at $2.5\ ^\circ$ C per minute.
(b) Find a complete equation for the model, giving the value of $B$ to 3 decimal places.

(3 marks)
Level 2 · 4 marksTry it