a Let x represent the number of hours Rafael walks and y represent the number of miles he is from home.
B
b The weekly wages can be viewed as the function's constant and the commission she earns on sold memberships is the variable. Also, is the function discrete of continuous?
C
c For the first four months, the function will resemble a step function.
A
aDiagram:
B
bDiagram:
C
cDiagram:
Practice makes perfect
a In our diagram we will let the x-axis represent time in hours and the y-axis Rafael's distance from his home in miles.
Rafael starts by walking for 15 minutes, which equals 0.25 hours, to the store that is 1 mile away. Given that he walks with a constant speed, the graph will increase linearly from the origin to the point (0.25,1) in our coordinate plane.
Next, Rafael shops for 30 minutes which means his distance from his home does not change for a total of 45 minutes, or 0.75 hours, that Rafael has been away. This gives us a third data point at (0.75,1). We also know that Rafael waits for the bus for an unknown period of time. To make things simple, we will assume that he waits for 0.1 hours, or 6 minutes, which gives us a fourth data point at (0.9,1).
Finally, Rafael is taking the bus home. We have not been given any information on how fast the bus drives. However, if we assume that the bus stops right outside of Rafael's home, the bus drives with a constant speed, and that Rafael's is away for a total of 1 hour, then we can plot a final data point at (1,0).
b From the exercise, we know that Sujata works 15 hours a week, making $9 per hour. Provided that she always works this number of hours, her weekly wages can be viewed as our graph's constant.
$15* 9=$135
Sujata's fixed wages per week are $135, which can be interpreted as the data point (0,135). She also makes $10 per gym membership she sells. If she sells x memberships, she will have earned an additional $10x. With this information, we can write our function.
y=10x+135
This is a linear function with a slope of 10 and a y-intercept of 135. However, notice that we cannot draw a continuous curve as she cannot sell fractions of a membership. Therefore, the function is actually an arithmetic sequence with a common difference of 10.
c From the exercise, we know that Tom begins with $500 and deposits his earnings by $150 on the last day of each month. Therefore, the function will begin as a step function for the first 4 months when the deposit is still below $1000.
The fourth time Tom deposits money into the account his balance will exceed $1000, which means he now earn interest. Note that we do not know if he continues to deposit money into the account after he has reached $1000. If we assume he does not, the function will now increase exponentially.
