Cooling process - Exponential functions

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SUMMARY

The discussion centers on the cooling process modeled by the equation y=28.49e^(-0.03890*800) + 26.51. The key takeaway is that the exponential function, represented by e^(-kt), will never cross the x-axis due to the nature of exponential decay, as confirmed by the equation T=T(initial)*e^(-kt)+T(room). The constant term 26.51 ensures that the function remains above zero, indicating that y will never equal zero.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with the TI-84 graphing calculator
  • Basic knowledge of cooling laws in physics
  • Ability to manipulate and solve equations involving exponentials
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  • Explore the mathematical properties of exponential decay functions
  • Learn how to graph exponential functions using the TI-84 calculator
  • Study Newton's Law of Cooling and its applications
  • Investigate the implications of asymptotic behavior in exponential models
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Students in physics or mathematics, educators teaching exponential functions, and anyone involved in experiments related to cooling processes.

Svensken
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Homework Statement



Hello i am doing a cooling experiment and i want to know the following:

y=28.49e^(-0.03890*800) +26.51 (note the 26.51) is not part of the exponential.

What is y? and I was wondering whether this would go ever go through the x axis?

Thanks people!

Homework Equations



T=T(initial)*e^(-kt)+T(room)

The Attempt at a Solution



I have been putting the info into my calculator and i just can't seem to be able to graph it (TI-84) and from my knowledge of exponentials i don't think that an exponential like this can be below the x axis, but i may very well be wrong.

Thanks again
-Svensken
 
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When y=0

Aekx+B= 0 ⇒ ekx=-B/A

and ekx is never less than zero for all values of x. Thus it does not cross the x-axis.
 
Last edited:
Thanks mate!
 

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