Exponential
and logarithmic functions are the most common types of functions which
exist in the world around us. As a result there are many problems which may require
the use of exponential or logarithmic equations in order to solve
them.
One example of this
is the Richter scale, which measures the magnitude M of
an earthquake according to the amplitude of its surface waves A
Hence: M=log A+C
where C =3.3+1.66 logDlogT
is a constant which depends on the period of time that the waves are
registered on the seismograph T and the distance from the
epicenter in angular degrees D. If we want to calculate the
amplitude (intensity) of the seismic wave we would need to solve a
logarithmic equation.
We would also need to
solve equations if we wanted to find the necessary time in hours (t)
for the amount of bacteria Escherichia coli, found in the intestinal tract
of many mammals, to reach a certain number.
(P=P_{0}.2^{t/D}
where P= 8000 bacteria, P_{0 }=500 D=30).
In the same way, if
we wanted to work out the age of a bone found at an archaeological
dig, and we knew that it contained 20% of carbon 14, which is present
in all animal life, we would need to solve the equation: 0.2=e^{0.000121t
}.^{ }
