Q 42. - Precalculus Enhanced with Graphing Utilities

Question

Match each of the following functions with the graph that best describes the situation.

(a) The temperature of a bowl of soup as a function of time.

(b) The number of hours of daylight per day over a 2-year period

(c) The population of Texas as a function of time.

(d) The distance traveled by a car going at a constant velocity as a function of time.

(e) The height of a golf ball hit with a 7-iron as a function of time.

Step-by-Step Solution

Answer

Part (a) The graph (II) represent the situation temperature of a bowl of soup as a function of time.

Part  (b) The graph (V) represent the situation number of hours of daylight per day over a 2-year period.

Part  (c) The graph (IV) represent the population of Texas as a function of time.

Part  (d) The graph (III) represent the situation distance traveled by a car going at a constant velocity as a function of time.

Part  (e) The graph (I) represent the height of a golf ball hit with a 7-iron as a function of time.

Part (a) Step 1. Given information.

We have given,

and 

(a) The temperature of a bowl of soup as a function of time.

(b) The number of hours of daylight per day over a 2-year period.

(c) The population of Texas as a function of time.

(d) The distance traveled by a car going at a constant velocity as a function of time.

(e) The height of a golf ball hit with a 7-iron as a function of time.

Part (a) Step 2. Concept used.

A position- time graph:

A position- time graph shows how far an object has traveled from its starting position at any given time since it started moving. 

Part (a) Step 3. Explanation.

We have, 

The temperature of a bowl of soup as a function of time. 

Temperature of the bowl decreases time is increases.

This situation represent the graph (II).

Part (a) Step 4. Conclusion.

Hence, graph  

represent the situation temperature of a bowl of soup as a function of time. 

Part (b) Step 1. Explanation.

We have,

The number of hours of daylight per day over a 2-year period.

This is the swing situation and its represent the graph (V).

Part (b) Step 2. Conclusion.

Hence, the graph

Represent the situation number of hours of daylight per day over a 2-year period.

Part (c) Step 1. Explanation.

We have,

The population of Texas as a function of time. 

When time increases the corresponding population of the Texas is also increases.

Part (c) Step 2. Conclusion.

Hence, the graph

Represent the situation  population of Texas as a function of time. 

Part (d) Step 1. Explanation.

We have,

The distance traveled by a car going at a constant velocity as a function of time. 

When time increases the distance traveled by graph is also increases.

This situation represent the graph,

Part (d) Step 2. Conclusion.

Hence the graph 

represent the situation distance traveled by a car going at a constant velocity as a function of time. 

Part (e) Step 1. Explanation.

We have,

The height of a golf ball hit with a 7-iron as a function of time. 

Height of the golf ball hit with a 7 iron is increases and then decreases.

This situation represent the graph 

Part (e) Step 2. Conclusion.

Hence the graph 

Represent the situation  height of a golf ball hit with a 7-iron as a function of time.