System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.23P
To determine

(a)

The given data and determine the best function.

Expert Solution
Check Mark

Answer to Problem 1.23P

Plot for the given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  1

The function is linear and given by:

y=50x1250.

Explanation of Solution

Given Information:

Data is given by:

x:2530354045y:02505007501000.

Calculation:

From the given data plot is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  2

From this plot, it is known that the function is linear with slope:

a=100004525a=50

So, the output function:

y=ax+by=50x+b (1)

Substitute the first pair of values from given data:

0=50×250+bb=1250

Substitute this value in first equation:

y=50x1250.

Conclusion:

Plot for the given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  3

The function is linear and given by:

y=50x1250.

To determine

(b)

The given data and determine the best function.

Expert Solution
Check Mark

Answer to Problem 1.23P

Plot for given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  4

The output is power function, and is given by:

y=3639x0.97.

Explanation of Solution

Given Information:

Data is by:

x:2.533.544.555.5678910y:150012201050915810745690620520480410390.

Calculation:

Plot for the given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  5

The plot is not linear.

For getting linear relationship, we can take log to the input out output. So, the data becomes:

logx:0.39790.47710.54410.60210.65320.6990.77820.74040.84510.90310.95421logy:3.1763.0863.0212.9612.9082.8722.7922.8392.7162.6812.6132.591

Plot for this data:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  6

This plot is linear with slop:

a=2.5913.17610.3979a=0.97

So, the equation:

logy=alogx+blogy=0.97logx+b

Substitute a pair of values:

2.591=0.97×1+bb=3.561

So, the equation becomes:

logy=0.97logx+3.561logy=0.97logx+log3639y=3639x0.97.

Conclusion:

Plot for given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  7

The output is power function, and is given by:

y=3639x0.97.

To determine

(c)

The given data and determine the best function.

Expert Solution
Check Mark

Answer to Problem 1.23P

The plot for given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  8

Function is exponential, and is given by:

y=89.567×100.000337x.

Explanation of Solution

Given Information:

Data is by:

x:10002000300040005000y:41.218.628.623.921.86.

Calculation:

Plots for the given data,

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  9

This plot is not linear.

Take log of output, the data become,

x:10002000300040005000logy:1.61491.270.93550.59330.2659

Plots for these values:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  10

This plot is linear, and slope is:

a=0.26591.614950001000a=0.00033725

So,

logy=ax+blogy=0.00033725x+b

Substitute one pair of values:

1.6149=0.00033725×1000+bb=1.95215

So, equation becomes:

logy=0.00033725x+1.95215logy=0.00033725x×log10+log89.567y=89.567×100.000337x.

Conclusion:

The plot for given data is:

System Dynamics, Chapter 1, Problem 1.23P , additional homework tip  11

Function is exponential, and is given by:

y=89.567×100.000337x.

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Chapter 1 Solutions

System Dynamics

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