Finding the Rate of Change-Algebra1-Solved Examples

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

Solutions

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

Correct Answer is : 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

Solutions

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

Solutions

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

Solutions

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

$y$ = 250

$t$ + 2000.

Step: 5

$t$ = 12,

$y$ = 250

$12$ + 2000 = 3000 + 2000 = 5000.

Step: 6

So, the number of students in the year 1995 is 5000.

Correct Answer 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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Correct Answer is : 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

Solutions

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

Correct Answer is : 2

Solved Examples and Worksheet for Finding the Rate of Change

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HighSchool Math