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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.
Solved.