1) A gym charges a one-time sign-up fee and then a regular monthly fee. The cost of a membership as a function of the number of months as a member is shown for 2010 and 2011 on the graph.
a. What characteristics of the graph represent the sign-up fee and the monthly fee? What are those values for the 2010 line?
b. Ho did the membership costs change from 2010 to 2011? Explain how you can tell from the graphs.
2) A bicycle computer records each wheel rotation to calculate the total distance traveled. To set up the computer, you select a calibration constant based on the bicycle's wheel size. The computer multiplies this constant times the number of wheel rotations to find the total distance in miles. Write an equation where distance d in miles is a function of rotations n if the calibration constant is 1382. If the function is incorrect and your wheel is actually slightly smaller, how should the function change?
3) High demand cars that are also in low supply tend to retain their value better than other cars. The data in the table is for a car that won a resale value award.
Table shows~
Years: 1 3 5
Value(%): 84 64 44
a. Write a function to represent the change in the percentage of the car's value over time. Assume that the function is linear for the first 5 years.
b. According to your model, by what percent did the car's value drop the day it was purchased and driven off the lot?
c. Do you think the linear model would still be useful after 10 years? Explain why or why not.
d. Suppose you used months instead of years to write a function. How would your model change?
Please help and thank you.
1)
a. To determine the sign-up fee and the monthly fee from the graph, we need to identify the y-intercept and the slope of the lines. The y-intercept represents the sign-up fee, and the slope represents the monthly fee.
For the 2010 line, we can see that it intersects the y-axis (x = 0) at a certain point. The y-value at that point represents the sign-up fee.
b. To analyze how the membership costs changed from 2010 to 2011, we need to compare the graphs. Based on the graphs, if the line for 2011 is steeper than the line for 2010, it means that the monthly fee increased. If the lines have the same slope, it means the monthly fee remained the same. Similarly, if the 2011 line has a higher y-intercept than the 2010 line, it means the sign-up fee increased.
2) The equation where distance (d) in miles is a function of rotations (n) using a calibration constant of 1382 is:
d = 1382 * n.
If the wheel size is smaller than anticipated, the calibration constant needs to be adjusted to account for the smaller wheel size. In this case, the function should be:
d = k * n, where k is the adjusted calibration constant.
3)
a. Since the function is assumed to be linear for the first 5 years, we can use the formula for a linear function: y = mx + b. In this case, the years are the x-values, and the value percentages are the y-values. Let's assume the function is V(t), where V represents the value and t represents time in years. The function can be written as:
V(t) = mt + b, where m is the slope and b is the y-intercept.
Using the data from the table, we can find the slope:
m = (64 - 84) / (3 - 1) = -10
To find the y-intercept, we can choose any point on the line. Let's use the point (1, 84):
84 = -10 * 1 + b
b = 94
Therefore, the function representing the change in the percentage of the car's value over time is:
V(t) = -10t + 94
b. To find the percent by which the car's value dropped the day it was purchased and driven off the lot (t = 0), we substitute t = 0 into the function:
V(0) = -10 * 0 + 94
V(0) = 94
So, the car's value dropped by 94 percent when it was purchased and driven off the lot.
c. The linear model may not be useful after 10 years because it assumes a constant linear depreciation rate. In reality, after a certain time, the depreciation rate may slow down or vary. Non-linear factors such as wear and tear, technological advancements, and market demand can also impact the car's value.
d. If we used months instead of years, the model would need to account for the difference in time units. The equation would need to be adjusted to include a conversion factor from months to years. The slope and y-intercept could also change based on the data available for the car's value over months.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
Also, #1 has no graph. You cannot copy and paste here.