Cooling process - Exponential functions

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In a cooling experiment, the equation y=28.49e^(-0.03890*800) + 26.51 is analyzed to determine if it crosses the x-axis. The equation reflects a cooling process modeled by an exponential function, where the constant 26.51 indicates the room temperature. Calculations show that the exponential component, e^(-kt), cannot yield a negative value, confirming that y will never equal zero. Therefore, the function does not intersect the x-axis. The conclusion is that the cooling process described by this equation will always remain above the x-axis.
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!
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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