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Perplex
Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial Mathematics
Cartesian plane & linesFunction TheoryModelling
2D & 3D GeometryVoronoi Diagrams
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegration
Calculator Skills
Review VideosFormula BookletAll Study Sets
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Perplex

Modelling (Lesson 3/7)

Exponential Models

1 / 10

Discussion

Hank forgot about his project and prepared no experiment to perform in class today! He remembers that he packed soup for lunch and decides to monitor its temperature every ​2​ minutes as it cools. He plots temperature ​C, in Celsius, against time ​t, in minutes:

(a)

Describe a curve that would model the temperature of Hank's soup.

Solution:

A suitable model is a smooth, steadily decreasing curve which drops quickly at first and then more slowly, flattening out towards a constant temperature. In particular:


– At ​t=0​ the curve starts near ​85∘​C and falls steeply.

– As ​t​ increases the rate of cooling diminishes, so the graph “bends” and becomes less steep.

– By about ​t=40​ min it is almost horizontal, approaching a horizontal asymptote at around ​22∘​C.


Note, this shape—rapid initial decrease, then gradual leveling off to a constant value—is characteristic of exponential decay.

1 free

Modelling (Lesson 3/7)

Exponential Models

1 / 10

Discussion

Hank forgot about his project and prepared no experiment to perform in class today! He remembers that he packed soup for lunch and decides to monitor its temperature every ​2​ minutes as it cools. He plots temperature ​C, in Celsius, against time ​t, in minutes:

(a)

Describe a curve that would model the temperature of Hank's soup.

Solution:

A suitable model is a smooth, steadily decreasing curve which drops quickly at first and then more slowly, flattening out towards a constant temperature. In particular:


– At ​t=0​ the curve starts near ​85∘​C and falls steeply.

– As ​t​ increases the rate of cooling diminishes, so the graph “bends” and becomes less steep.

– By about ​t=40​ min it is almost horizontal, approaching a horizontal asymptote at around ​22∘​C.


Note, this shape—rapid initial decrease, then gradual leveling off to a constant value—is characteristic of exponential decay.

1 free