SOLUTION: Newton's Law of Cooling describes the way the temperature of objects adjusts to the ambient temperature over time. This relationship is an exponential function. Let H(1)=93(0.91)^

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Question 1006644: Newton's Law of Cooling describes the way the temperature of objects adjusts to the ambient temperature over time. This relationship is an exponential function. Let H(1)=93(0.91)^t+68 describe the temperature of a beverage (in degrees F)t minutes after a 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?
b. What is the asymptote of the graph of H(t) and what does it mean in the context of this problem?
c. Sketch a rough graph of H(t).
d. Calculate the coordinates of the y-intercept of H(1). What do they mean in the context of the problem?
e. What is the range of H(t)?
f. What is the value of H (10)and what meaning does it have in context?
g. Exactly when does the temperature hit 90 degrees? Solve with logs.
g. Exactly when does the temperature hit 75 degrees? Solve with logs.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Newton's Law of Cooling describes the way the temperature of objects adjusts to the ambient temperature over time. This relationship is an exponential function. Let H(t)= 93(0.91)^t+68 describe the temperature of a beverage (in degrees F)t minutes after a 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? Hot coffee because the temperature is 93*1+68 when time = zero.
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b. What is the asymptote of the graph of H(t) and what does it mean in the context of this problem? H(t) = 68. Coffee cools till it reaches room temp.
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c. Sketch a rough graph of H(t).
graph%28400%2C400%2C-10%2C60%2C-10%2C100%2C93%280.91%29%5Ex%2B68%29
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I'll leave the rest to you.
Cheers,
Stan H.
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d. Calculate the coordinates of the y-intercept of H(1). What do they mean in the context of the problem?
e. What is the range of H(t)?
f. What is the value of H (10)and what meaning does it have in context?
g. Exactly when does the temperature hit 90 degrees? Solve with logs.
g. Exactly when does the temperature hit 75 degrees? Solve with logs.