Solved Examples and Worksheet for Finding the Rate of Change

Q1The table shows the number of girls admitted in a school in two consecutive years. Assuming the same rate of change for the students admitted in subsequent years, estimate the number of girls admitted in the year 2003.
 Year Number of girls 1998 2400 1999 3000

A. 4800
B. 5400
C. 6000
D. 4200

Step: 1
Average rate of change = Change in the number of girls admitted in schoolChange in time
Step: 2
= 3000-24001999-1998
Step: 3
= 600 per year
Step: 4
So, the number of girls admitted in the year 2003 is 2400 + 5(600) = 5400
Q2The annual income of Jeff in 1996 was $30,000. His income rose to$36,000 in 1998. At this rate what would be the annual income of Jeff in 2004?

A. $42,000 B.$54,000
C. $60,000 D.$57,000

Step: 1
Average rate of change = Change in the annual incomeChange in time
Step: 2
= 36000-300001998-1996
Step: 3
= 60002 = $3000 per year Step: 4 So, the annual income of Jeff in the year 2004 is$(30,000 + 8(3,000)) = $54,000 Correct Answer is :$54,000
Q3Find the value of y when x = 2.38 using the relation between x and y given in the following data.
 Input(x) - 1.2 0 0.6 1.5 2.4 3.1 3.6 Output(y) 3.2 2 1.4 0.5 - 0.4 - 1.1 - 1.6

A. 0.42
B. 0.36
C. - 0.38
D. 0.38

Step: 1
Rate of change = change in output valueschange in input values
Step: 2
 Input Output Change in input values Change in output values Rate of change - 1.2 3.2 0 2 1.2 - 1.2 - 1 0.6 1.4 0.6 - 0.6 - 1 1.5 0.5 0.9 - 0.9 - 1 2.4 - 0.4 0.9 - 0.9 - 1 3.1 - 1.1 0.7 - 0.7 - 1 3.6 - 1.6 0.5 - 0.5 - 1
Step: 3
The rate of change = - 1
Step: 4
The linear equation that represents the data is y = 2 + (- 1) x.
Step: 5
y = 2 - x
Step: 6
When x = 2.38, y = - 0.38.
Correct Answer is :   - 0.38
Q4From 1983 through 1997, the number of students in a school is increased by about 250 per year. In 1983, there were 2000 students. Find the number of students in the year 1995.

A. 5000
B. 4000
C. 7000
D. 8000

Step: 1
The rate of increase is 250 per year.
Step: 2
Let t = 0 represent the year 1983.
Step: 3
The year 1995 is represented by t = 12.
Step: 4
This situation is represented by the linear equation y = 250t + 2000.
Step: 5
At t = 12, y = 250(12) + 2000 = 3000 + 2000 = 5000.
Step: 6
So, the number of students in the year 1995 is 5000.
Q5The following table shows Eddy's earnings for the number of hours he works over time. How many hours does he need to work to earn $119?  Hours 1 2 3 4 5 Earnings 35 42 49 56 63 A. 10 B. 11 C. 8 D. 12 Step: 1 Rate of change = 42 - 352 - 1 = 7. Step: 2 This situation can be modeled by the linear equation y = 7 t + 28. Step: 3 119 = 7 t + 28 gives t = 13. Step: 4 Eddy needs to work for 13 hours. Correct Answer is : 12 Q6The table shows the temperatures at different altitudes. Find the rate of change of temperature.  Temperature(°C) 10.5 8 5 0 Altitude(in m) 800 1300 1900 2900 A. 2 B. - 0.005 C. 0.05 D. 0.005 Step: 1 Rate of change of temperature = Change in temperatureChange in altitude = 8 - 10.51300 - 800 Step: 2 = - 2.5500 Step: 3 = - 1200 Step: 4 = - 0.005 Step: 5 So, the rate of change of temperature is - 0.005. Correct Answer is : - 0.005 Q7The table shows the profits(in million$) of a company since 2000. Find the rate of change of profit.
 Profit(in million $) 59 71 83 95 Years since 2000 1 2 3 4 A. 12 B. 2 C. 15 D. 5 Step: 1 Rate of change of profit = Change in profitChange in year = 71 - 592 - 1 Step: 2 = 121 Step: 3 = 12 Step: 4 So, the rate of change of profit is 12. Correct Answer is : 12 Q8The table shows the salaries(in$) of Chris since 1997. Find the rate of change of salary.
 Salary(in $) 1500 2100 2700 3300 Years since 1997 1 2 3 4 A.$600
B. $150 C.$500
D. $200 Step: 1 Rate of change of salary = Change in salaryChange in year = 2100 - 15002 - 1 Step: 2 = 6001 Step: 3 = 600 Step: 4 So, the rate of change of salary is 600. Correct Answer is :$600
Q9The table shows the numbers of men participants at Boston Marathon from the year 2001 to 2006. Find the rate of change between 2002 to 2005.

A. 500
B. 508.3
C. 608.3
D. 580.3

Step: 1
The rate that describes how one quantity changes in relation to another is called rate of change.
Step: 2
Rate of change = change in participantschange in year = 10889 - 91482005 - 2002
Step: 3
= 17413
Step: 4
= 580.3
Q10The ages of students in Mr.David′s class is shown in the table. What is the rate of change of students from age 13 to 15?

A. 3
B. 4
C. 5
D. 2

Step: 1
The rate that describes how one quantity changes in relation to another is called rate of change.
Step: 2
Rate of change = change in number of studentschange in age = 20 - 1615 - 13
Step: 3
= 42
Step: 4
= 2