1 Newtons Law of Cooling describes the way temperatures of o

1. Newton’s Law of Cooling describes the way temperatures of objects adjust to the ambient temperature over time. This relationship is an exponential function. Let H(x)=93(0.91t)+68 describes the temperature of a beverage (in degrees F) t minutes after Dunkin’ Donuts employee hands it to you.

a) Is the beverage hot coffee or iced coffee (how can you tell by looking at the equation)? ALSO, What is the asymptote of the graph of H(t) and what does it mean in context of this problem?

Solution

It is a cooling case because a hot beverage cools down

So, the beverage is hot coffee..

Also, from the equation, that 0.91^t part ofthe equation is a decreading function because as t increases, 0.91^t decreases, so what happens is that with increase in time, the temperature decreases.

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Asymptote :
When t ---> inf , 0.91^t tends to 0
And thus 93(0) + 68 approx becomes 68

So, the horiz asymptote is 68

In the context of this prob, this is the steady state temperature of the beverage after a larger period of time... Another way of putting this is that the 68 is simply the temperature of the surroundings or the ambient temperature