Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

602 Chapter 18 Mathematics in Engineering

n

1 2.000000

2 2.250000

5 2.488320

10 2.593742

20 2.653298

50 2.691588

100 2.704814

200 2.711517

500 2.715569

1000 2.716924

2000 2.717603

5000 2.718010

10000 2.718146

a 1 

1

n

b

n

xf(x)  2

x

f(x) e

x

f(x)  3

x

0 1 1.00 1.00

0.2 1.15 1.22 1.25

0.4 1.32 1.49 1.55

0.6 1.52 1.82 1.93

0.8 1.74 2.23 2.41

1 2.00 2.72 3.00

1.2 2.30 3.32 3.74

1.4 2.64 4.06 4.66

1.6 3.03 4.95 5.80

1.8 3.48 6.05 7.22

2 4.00 7.39 9.00

2.2 4.59 9.03 11.21

2.4 5.28 11.02 13.97

2.6 6.06 13.46 17.40

2.8 6.96 16.44 21.67

3 8.00 20.09 27.00

3.2 9.19 24.53 33.63

3.4 10.56 29.96 41.90

3.6 12.13 36.60 52.20

3.8 13.93 44.70 65.02

4 16.00 54.60 81.00

f

(x

)

90

80

70

60

50

40

30

20

10

0

01234

x

2 x

ex

3 x

■Figure 18.13 The comparison of functions 2

x

, e

x

,and 3

x

.

AsnSq2.7182818285....

The exponential functions have important characteristics, as demonstrated by examples

shown in Table 18.5. Example 1 shows the changes that occur in a exponential model when the

growth rate of an exponential function increases. Example 2 demonstrates similar changes for a

decaying exponential function. Note these important effects as you study Table 18.5.

A good understanding of these concepts will be beneficial when you take future engineering classes.

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