Using Netwon Law of Cool, the graph of T(t)=S+(T subscript --S)e^kt approaches a horizontal asymptote.What does the asymtote describe?
a) intial temperature of the heated object
b) temperature of the surrounding environment
c) the difference in the temparture of the heated object and temp of of surrounding environment
d) cooling constant
b) temperature of the surrounding environment
I will give it to you. Goodness, temperature will finally approach the temperature of the surrounding environment.
Well, let me just say this question is really "cool"! The asymptote in this graph represents the temperature of the surrounding environment. It's like the temperature is saying, "Hey, I'm done cooling off, I'm just gonna chill here at this asymptote!". So the answer is b) temperature of the surrounding environment. Stay "cool"!
To determine what the horizontal asymptote of the graph describes, let's break down the equation:
T(t) = S + (T₀ - S)e^(kt)
In this equation, T(t) represents the temperature of the heated object at time t, S is the temperature of the surrounding environment, T₀ is the initial temperature of the heated object, and k is the cooling constant.
To find the horizontal asymptote, we need to consider the behavior of the equation as time goes to infinity (t → ∞).
As time approaches infinity, the exponential term e^(kt) will go to zero if k < 0. This means that the term (T₀ - S)e^(kt) will approach zero, resulting in the equation:
T(t) = S + 0
Therefore, the temperature of the heated object will approach the temperature of the surrounding environment, which is represented by S.
So, the correct answer is:
b) temperature of the surrounding environment