Match each of the following functions with the graph that...

Match each of the following functions with the graph that best describes the situation. $$ \begin{array}{l}{\text { (a) The temperature of a bowl of soup as a function of time }} \\ {\text { (b) The number of hours of daylight per day over a } 2 \text { -year period }} \\ {\text { (c) The population of Florida as a function of time }} \\ {\text { (d) The distance traveled by a car going at a constant velocity as a function of time }} \\ {\text { (e) The height of a golf ball hit with a } 7 \text { -iron as a function of time }}\end{array} $$

Match each of the following functions with the graph that best describes the situation.
$$
\begin{array}{l}{\text { (a) The temperature of a bowl of soup as a function of time }} \\ {\text { (b) The number of hours of daylight per day over a } 2 \text { -year period }} \\ {\text { (c) The population of Florida as a function of time }} \\ {\text { (d) The distance traveled by a car going at a constant velocity as a function of time }} \\ {\text { (e) The height of a golf ball hit with a } 7 \text { -iron as a function of time }}\end{array}
$$

Key Concepts

Exponential Decay

Exponential decay describes a process in which the rate of decrease of a quantity is proportional to its current value. This concept is used to model scenarios where a quantity gradually decreases over time and often approaches a limiting value. In physical situations like cooling, the temperature drops rapidly at first and then more slowly as it approaches the ambient temperature.

Periodic Functions

Periodic functions are mathematical functions that repeat their values in regular intervals or periods. They are often used to model phenomena that have cyclical behavior, such as seasonal variations or diurnal cycles. The repeating pattern in these functions makes them ideal for representing data like changes in daylight hours over the course of a year.

Exponential Growth

Exponential growth occurs when the increase in a quantity is proportional to the current amount, leading to rapid increases over time. This type of function is commonly used to model populations or investments where the accumulated amount accelerates as it grows, reflecting compounding effects.

Linear Functions

Linear functions represent relationships where the rate of change is constant, resulting in a straight-line graph. They are typically used to model situations with constant rates such as uniform motion, where the distance increases steadily over time with a fixed velocity.

Quadratic Functions

Quadratic functions are characterized by a parabolic shape and are common in modeling situations where there is acceleration involved, such as projectile motion. These functions typically produce a curve that rises to a maximum point before descending, capturing both the ascent and descent phases of the motion.

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