Understanding Engineering Mathematics

currentIis approximately exponential, i.e

I Ioexp

(

eV

kT

)

In the general case obtain an expression forV in terms ofI.
3.The speed,v, of the signal in a submarine cable depends on the radiusR, in mm, of
the cable’s covering according to

v=

16

R^2

ln

(

R

4

)

Plot the graph of this function fromR=4mmtoR=12 mm. Estimate the maximum

speed, and the value ofRfor which this occurs.

4.According to Benford’s law (an American physicist who noticed that in his university
library the first pages of the now old fashioned tables of logarithms were more worn
than the rest) the probability that a number drawn randomly from a sufficiently smooth
range of numbers spread over several orders of magnitudes begins with the digitnis

P(n)=log 10 (n+ 1 )−log 10 n

Plot this function forn=1 to 9. Discuss the implications and conduct some experiments

to see if the results agree with experience.

Answers to reinforcement exercises

4.3.1 y=an,n=an integer

A. and B.
y

0 x

1

y = e^4 x y^ = e^3 x

is y = px which is

very close to y = e^3 x

Note that 3<π<4.