Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex

    Modelling (Lesson 5/10)

    Exponential Models

    1 / 9

    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:

    Powered by Desmos

    (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.