options: Define, evaluate, and compare functions.

Interpret expressions for functions in terms of the situation they model.

Analyze functions using different representations.

Build new functions from existing functions.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

Interpret functions that arise in applications in terms of the context.
problem_activity: Task
A cup of hot coffee will, over time, cool down to room temperature.  The
principle of physics governing the process is Newton's Law of Cooling.
Experiments with a covered cup of coffee show that the temperature (in
degrees Fahrenheit) of the coffee can be modelled by the following
equation
$$
f(t) =  110e^{-0.08t}+75.
$$
Here the time $t$ is measured in minutes after the coffee was poured into
the cup.
Explain, using the structure of the expression $110e^{-0.08t} + 75$,
why the coffee temperature decreases as time elapses.
What is the temperature of the coffee at the beginning of the experiment?
After how many minutes is the coffee $140$ degrees?
After how many minutes is the coffee $100$ degrees?


correct_option_index: 1

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