Height Above Canyon Floor
Time (minutes)
360
280
3
160
10
80
14
Which statement best interprets the rate of change of the linear model shown in the table?
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking up from
• canyon floor changes at a rate of - 20 feet per minute.
The elevation of a hiker
• who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking down to a
• canyon floor changes at a rate of - 20 feet per minute.
The best interpretation of the rate of change of the linear model shown in the table is: The elevation of a hiker who is hiking down to a canyon floor changes at a rate of -20 feet per minute.
Number of Months Cost ($)
1
74
2
99
3
124
4
149
The table below shows the cost for a gym membership at the local fitness center with an initial start-up fee charged in the first month. Find the slope, or monthly cost.
$49
• $74
• $25
• $37.25
To find the slope, we need to determine the change in cost per change in month.
For example, between month 1 and month 2, the cost increases from $74 to $99 => a change of $99 - $74 = $25.
So, the slope, or monthly cost, is $25.
A linear graph of parking fees in dollars based on hours parked has the points (2, 20) and (6,44). How would you interpret the slope of the graph as the rate of change in the parking fee for each additional hour of parking?
The parking fee rises by
• $8 with each additional hour.
The parking fee rises by
• $10 with each additional hour.
The parking fee rises by
• $6 with each additional hour.
The parking fee rises by
• $7.33 with each additional hour.
To find the slope, we can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y (parking fee) is $44 - $20 = $24, and the change in x (hours parked) is 6 - 2 = 4.
So, the slope is:
slope = $24 / 4 = $6
Therefore, the correct interpretation is: The parking fee rises by $6 with each additional hour.
To determine the rate of change from the given data in the table, we need to compare the change in elevation with the change in time.
Looking at the table, we can see that as the time increases, the elevation decreases. This suggests that the hiker is descending down to the canyon floor.
To calculate the rate of change, we can compare the change in elevation with the change in time.
From 360 to 280, the elevation decreases by 80 feet in 3 minutes, giving a rate of change of -80/3 = -26.67 feet per minute.
From 280 to 160, the elevation decreases by 120 feet in 10 minutes, giving a rate of change of -120/10 = -12 feet per minute.
From 160 to 80, the elevation decreases by 80 feet in 4 minutes, giving a rate of change of -80/4 = -20 feet per minute.
We can see that the rate of change of the linear model is consistent at around -20 feet per minute.
Therefore, the correct statement to interpret the rate of change of the linear model would be:
" The elevation of a hiker who is hiking down to a canyon floor changes at a rate of -20 feet per minute."