Hilda owns several hens on her family

MAP4C Lesson 12 Assignment
In this assignment you are going to explore the characteristics of applications related to linear functions
Part A: Finding the Answer
In this section, you are going to use the formula for calculating rates of change
For each question, answer the question giving the clues that you used in determining your answer. You will be given three
marks – two marks for your correct clues and one mark for the correct answer.
_Constant___ 1. The rate of change of this graph is (increasing, decreasing or constant)?
__16 km/hr__ 2. Molly roller blades at a constant speed, travelling 8 km from her home to the library in 0.5 h.
What was the rate of change of distance with respect to time?
__Constant__ 3. Hilda owns several hens on her family’s farm. She decides to record the total number of eggs
produced by the hens over a given time period. The rate of change of the total number of eggs with respect to
the number of days is (increasing, decreasing, constant)?
Page 1
The rate of change for the graph is
constant as it is a straight line.
8/0.5 = 16 km/ hr.
Hint: create an equation using y=mx + b
Use point (4,25) and (0,0)
As the graph of total number of eggs pro-
duced by the hens is a straight line, the rate
of change is constant.

__20__ 4. Hilda owns several hens on her family’s farm. She decides to record the total number of eggs produced by the
hens over a given time period. How many days after Hilda starts counting the eggs will there be 84 eggs
produced?
__Constant__ 5. Kandeer measures the amount of water in his backyard well each day during a dry spell in his
area. Here is the data collected. Create a graph to show the data
Day 0 1 2 3 4 5 6 7
Amount of
Water (L)
50 46 42 38 34 30 26 22
The rate of change of the amount of water with respect to the number of days is (increasing, decreasing,
constant)?
___-4_ 6. Kandeer measures the amount of water in his backyard well each day during a dry spell in his area.
Day 0 1 2 3 4 5 6 7
Amount of
Water (L)
50 46 42 38 34 30 26 22
Using the rate of change formula, find the rate of change. The rate of change of the amount of water with
respect to the number of days is
Page 2
Slope of the line: (0-25)/(0-4) = 4.25
Equation of the line: y = 4.25 x
When y = 84, x= 84/ 4.25 = 19.76 = 20 days
(approx.)
0 1 2 3 4 5 6 7 8
0
20
40
60
Water vs no of days
Rate of change: (46-50)/(1-0) = -4

_13 days___ 7. Kandeer measures the amount of water in his backyard well each day during a dry spell in his
area.
Day 0 1 2 3 4 5 6 7
Amount of
Water (L)
50 46 42 38 34 30 26 22
If the pattern continues, how many days will pass until the well is empty? Answer this question by expanding
the graph you created in #5
_0.07___8. Pierre invested the earnings from his summer job in shares of a technology stock. The table shows the value
of a share at the end of each week for six weeks.
Week 0 1 2 3 4 5 6
Share
Value ($)
1.08 1.15 1.22 1.29 1.36 1.43 1.50
What is the rate of change of share value with respect to time?
_20 weeks___ 9. Pierre invested the earnings from his summer job in shares of a technology stock. The table
shows the value of a share at the end of each week for six weeks.
Week 0 1 2 3 4 5 6
Share
Value ($)
1.08 1.15 1.22 1.29 1.36 1.43 1.50
If the pattern continues, after how many weeks will the share value first exceed $2.50?
Page 3
0= -4x+50
X= 12.5
The well will dry up after 13 days
Rate of change: (1.15-1.08)/ (1-0) = 0.07
Y= 0.07x +1.08
2.5=0.07x+1.08
X= 20.28 i.e approximately after 20 weeks