Math Concept:The average rate of change is calculated as the difference of the y's over the difference of the x's over some interval.That formula should look familiar because it is the slope; they are the same thing!f (b) – f (a)Y2 - y1A. R.C.=It is often viewed as a new unit and used in many other instances.b — аX2 – X1For example, think of miles per hour (mph or mi/h); this is simply the change in miles over the change in hours.рayment:$200.00payment:$150.00payment:$100.00рayment:$50.00MonthBalanceMonthBalanceMonthBalanceMonthBalance$1,783.34$1,722.71$1,660.74$1,597.40$1,532.66$1,466.49$1,398.87$1,329.75$1,259.10$1,186.89$1,113.09$1,037.67$960.57$881.78$801.24$718.93$634.80$548.81$460.93$371.10$279.30$185.46$89.56-$8.47$1,783.34$1,622.71$1,458.53$1,290.73$1,119.22$943.93$764.76$581.64$394.48$203.19$7.68-$192.15$1,783.34$1,672.71$1,559.63$1,444.06$1,325.94$1,205.21$1,081.81$955.69$826.79$1,783.34$1,772.71$1,761.84$1,750.73$1,739.38$1,727.78$1,715.92$1,703.80$1,691.41$1,678.75$1,665.80$1,652.58$1,639.06$1,625.24$1,611.12$1,596.68$1,581.93$1,566.85$1,551.44$1,535.69$1,519.59$1,503.13$1,486.31$1,469.12$1,451.551111222233444566.6777788.88$695.04$560.39$422.76$282.09$138.32-$8.63999101010101111111112121213131314141415151616171718181919202021212222232324Calculating the Average Rate of Change (A.R.C.) of the Balance:difference in Balance:difference in Balance:difference in Months:now divide them:difference in Balance:difference in Balance:difference in Months:difference in Months:difference in Months:now divide them:now divide them:now divide them:

Math Concept: The average rate of change is calculated as the difference of the y's over the difference of the x's over some interval. That formula should look familiar because it is the slope; they are the same thing! It is often viewed as a new unit and used in many other instances. For example, think of miles per hour (mph or mi/h); this is simply the change in miles over the change in hours. f(b) - f(a) Y2 - Y1 A. R.C.= b - a X2 - X1 payment: $200.00 |рayment: $150.00 payment: $100.00 payment: $50.00 Month Balance Month Balance Month Balance Month Balance $1,783.34 $1,622.71 $1,783.34 $1,672.71 $1,783.34 $1,783.34 $1,722.71 $1,660.74 $1,597.40 $1,532.66 $1,466.49 $1,398.87 $1,329.75 $1,772.71 $1,761.84 1 2 $1,458.53 2 $1,559.63 2 2 3 $1,290,73 3 $1,444.06 3 3 $1,750.73 $1,739.38 $1,727.78 $1,715.92 $1,703.80 $1,691.41 $1,678.75 $1,665.80 $1,652.58 $1,639.06 $1,625.24 $1,611.12 $1,596.68 $1,581.93 $1,566.85 $1,551.44 $1,535.69 $1,519.59 $1,503.13 $1,486.31 $1,469.12 $1,451.55 4 $1,119.22 4 $1,325.94 4 4 $943.93 $1,205.21 5 $764.76 $581.64 $1,081.81 $955.69 6 6 6 6 7 7 7 $1,259.10 $1,186.89 8 $394.48 8 $826.79 8. 9| $203.19 $7.68 -$192.15 9 $695.04 $560.39 $422.76 $282.09 $138.32 $1,113.09 $1,037.67 $960.57 $881.78 10 10 10 10 11 11 11 11 12 12 12 13 13 13 $801.24 $718.93 14 -$8.63 14 14 15 15 16 $634.80 16 17 $548.81 17 $460.93 $371.10 $279.30 $185.46 18 18 19 19 20 20 21 21 $89.56 -$8.47 22 22 23 23 24 Calculating the Average Rate of Change (A.R.C.) of the Balance: difference in Balance: difference in Months: now divide them: difference in Balance: difference in Balance: difference in Balance: difference in Months: now divide them: difference in Months: difference in Months: now divide them:| now divide them:

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Math Concept:
The average rate of change is calculated as the difference of the y's over the difference of the x's over some interval.
That formula should look familiar because it is the slope; they are the same thing!
f (b) – f (a)
Y2 - y1
A. R.C.=
It is often viewed as a new unit and used in many other instances.
b — а
X2 – X1
For example, think of miles per hour (mph or mi/h); this is simply the change in miles over the change in hours.
рayment:
$200.00
payment:
$150.00
payment:
$100.00
рayment:
$50.00
Month
Balance
Month
Balance
Month
Balance
Month
Balance
$1,783.34
$1,722.71
$1,660.74
$1,597.40
$1,532.66
$1,466.49
$1,398.87
$1,329.75
$1,259.10
$1,186.89
$1,113.09
$1,037.67
$960.57
$881.78
$801.24
$718.93
$634.80
$548.81
$460.93
$371.10
$279.30
$185.46
$89.56
-$8.47
$1,783.34
$1,622.71
$1,458.53
$1,290.73
$1,119.22
$943.93
$764.76
$581.64
$394.48
$203.19
$7.68
-$192.15
$1,783.34
$1,672.71
$1,559.63
$1,444.06
$1,325.94
$1,205.21
$1,081.81
$955.69
$826.79
$1,783.34
$1,772.71
$1,761.84
$1,750.73
$1,739.38
$1,727.78
$1,715.92
$1,703.80
$1,691.41
$1,678.75
$1,665.80
$1,652.58
$1,639.06
$1,625.24
$1,611.12
$1,596.68
$1,581.93
$1,566.85
$1,551.44
$1,535.69
$1,519.59
$1,503.13
$1,486.31
$1,469.12
$1,451.55
1
1
1
1
2
2
2
2
3
3
4
4
4
5
6
6.
6
7
7
7
7
8
8.
8
8
$695.04
$560.39
$422.76
$282.09
$138.32
-$8.63
9
9
9
10
10
10
10
11
11
11
11
12
12
12
13
13
13
14
14
14
15
15
16
16
17
17
18
18
19
19
20
20
21
21
22
22
23
23
24
Calculating the Average Rate of Change (A.R.C.) of the Balance:
difference in Balance:
difference in Balance:
difference in Months:
now divide them:
difference in Balance:
difference in Balance:
difference in Months:
difference in Months:
difference in Months:
now divide them:
now divide them:
now divide them:

Expert Solution

Step 1

Calculate the average rate of change of the balance for the first dataset starting from the first month to the last month

The first month is given as 0 and the last month is 11

The difference between the months is:

$\begin{array}{rcl} Difference between last and first months & = & 11 - 0 \\ = & 11 \end{array}$

The balance at the start of the first month 1783.34$ and the balance at the last month -192.15$

Difference between the balances is equal to

$\begin{array}{rcl} Difference in the balance between last and first months & = & 1783.43 - (- 192.15) \\ = & 1975.58 \end{array}$

Divide the obtained quantities to calculate the average rate of change in the balance

$\begin{array}{rcl} ARC & = & \frac{Difference in balances between first and last month}{Difference between the months} \\ = & \frac{1975.58}{11} \\ = & 179.598 \end{array}$

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