Cooling process - Exponential functions

In summary, the conversation is about a cooling experiment and the question of whether a specific equation will ever go through the x-axis. The equation in question is y=28.49e^(-0.03890*800) +26.51 and the individual is having trouble graphing it on their calculator. They are also wondering if this type of exponential equation can go below the x-axis. However, it is clarified that the equation will never cross the x-axis.
  • #1
Svensken
29
0

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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  • #2
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:
  • #3
Thanks mate!
 

1. How does the cooling process relate to exponential functions?

The cooling process can be modeled using an exponential function, where the temperature decreases at a constant rate over time. This is because the amount of heat lost per unit of time is proportional to the temperature difference between the object and its surroundings.

2. What is the formula for the cooling process using exponential functions?

The formula for the cooling process using exponential functions is T(t) = T0 * e-kt, where T(t) is the temperature at time t, T0 is the initial temperature, and k is the cooling constant.

3. How does the initial temperature affect the cooling process?

The initial temperature affects the cooling process by determining the starting point of the exponential curve. A higher initial temperature will result in a steeper decrease in temperature, while a lower initial temperature will result in a slower decrease.

4. What is the cooling constant and how does it impact the cooling process?

The cooling constant, represented by the letter k, is a measure of how quickly an object cools down. It is influenced by factors such as the material and shape of the object, as well as the surrounding temperature and pressure. A higher value of k means the object will cool down faster, while a lower value of k indicates a slower cooling process.

5. Can the cooling process be modeled using other functions besides exponential functions?

Yes, the cooling process can also be modeled using power functions, logarithmic functions, and polynomial functions. However, exponential functions are the most commonly used and accurate representation of the cooling process, especially for objects that cool down in a consistent environment.

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