SOLUTION: A caterer placed several bottles of soda in the refrigerator. The Temperature T of the bottles t minutes after they are placed in the refrigerator is given by:
T(t)=36+43e^-0.058
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-> SOLUTION: A caterer placed several bottles of soda in the refrigerator. The Temperature T of the bottles t minutes after they are placed in the refrigerator is given by:
T(t)=36+43e^-0.058
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Question 1200657: A caterer placed several bottles of soda in the refrigerator. The Temperature T of the bottles t minutes after they are placed in the refrigerator is given by:
T(t)=36+43e^-0.058t
What is the horizontal asymptote of T(t)? Interpret the horizontal asymptote in the context of the problem? You may want to graph the equation to find the horizontal asymptote. Found 3 solutions by greenestamps, ikleyn, math_tutor2020:Answer by greenestamps(13216) (Show Source):
Graphing the equation will show you the horizontal asymptote; however, you should be able to find the asymptote without graphing.
The equation is an exponential decay equation. The horizontal asymptote will be found by seeing what value the equation approaches as t gets very large. In this particular problem, the horizontal asymptote is the temperature of the soda after it has been in the refrigerator for "a long time".
Mathematically, when t gets large, approaches 0, so the horizontal asymptote is 36+0 = 36.
ANSWERS:
The horizontal asymptote is 36.
The meaning of the asymptote is that the temperature of the soda after it has been in the refrigerator for a long time will be 36 (presumably, 36 degrees F).
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A caterer placed several bottles of soda in the refrigerator.
The Temperature T of the bottles t minutes after they are placed in the refrigerator
is given by T(t)=36+43e^-0.058t
What is the horizontal asymptote of T(t)? Interpret the horizontal asymptote
in the context of the problem?
You may want to graph the equation to find the horizontal asymptote.
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For the analyzes, you should know that an exponential function with the base greater than 1
and with negative degree quickly becomes small and tends to zero as the degree tends to negative infinity.
It is why tends to zero as t ---> oo (infinity).
A constant positive coefficient (factor) at the exponent changes NOTHING in this
behavior, so tends to zero as t ---> oo (infinity).
Thus the temperature of the bottle T(t) tends to 36 degrees of Fahrenheit as t ---> oo.
It means that function T(t) = has horizontal asymptote = 36.
Obviously and clearly, 36°F is the temperature in the refrigerator.
The value 36 + 43 is the initial temperature of the bottle at t=0, when the bottle
was placed into the refrigerator and the timer started counting time.
It is what you should be able to extract from the given formula to interpret it in the given context.
It is what you should see and understand clearly from the first glance looking at this formula.
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