a How does gravity affect an object that is being thrown into the air?
B
b The amount of shoppers can vary greatly depending on the time of day.
C
c Temperature differences even out over time.
A
aExample Sketch:
Description: See solution.
B
bExample Sketch:
Description: See solution.
C
cExample Sketch:
Description: See solution.
Practice makes perfect
a To sketch this, we want to show the height of the ball on the vertical axis and the distance from the centerfield on the horizontal axis.
When the ball is thrown, the distance from centerfield is 0 feet. This places our first data point somewhere on the y-axis. The ball will initially have some height above the ground, based on the height of the player throwing the ball, so our first data point has to be above the origin. Let's use this information plot our first example data point.
The distance from centerfield increases as we move in the positive direction on the horizontal axis. Recall that when something is thrown, gravity causes a trajectory in the shape of a parabola. Let's assume that the ball is caught at about the same height as it was thrown from. We can plot a second data point and connect them with a curve.
Note that this is just one example of a graph that fits the situation.
b The sketch will show business hours on the horizontal axis and the number of shoppers on the vertical axis. We will assume that business hours for this shopping mall is between 8:00AM and 8:00PM.
The number of shoppers in the mall will depend on the time of day. For example, there will not be that many shoppers in the morning because people have to be at work. However, there will likely not be zero shoppers, either, as there is always someone that for whatever reason has free time and wants to shop.
There will be a continuous flow of shoppers in and out of the mall, so a graph that represents the number of shoppers will be a continuous curve. We can assume that the number of shoppers will peak around lunchtime and after usual work hours as office workers find time to shop. Let's use this information to sketch the scenario.
Note that this is just one example of a graph that fits the situation.
c Differences in temperatures even out over time. If there is a large difference in temperature between two objects, the temperature of the hotter object will drop faster then if the temperatures are closer together. Let's sketch a curve that resembles exponential decay. The curve will drop off until the coffee is room temperature.
Note that this is just one example of a graph that fits the situation.
