2. Introduction..
▶ Statement:-
▶ The rate of change of population is directly proportional
to the amount of population.
▶The law of natural growth and decay is one of the applications
of integrals, which helps to understand how a quantity varies
relative to its size.
▶ Formula for natural growth and decay:-
f(x) = a(1 + r)t, and f(x) = a(1 - r)t.
3. Explanation:-
▶ Growth and decay refer to the direction in which a quantity ischanging. If
something isgrowing, itmeansthata value isincreasing.
▶ I
fsomething isdecaying, itmeansthata value isdecreasing.
▶ The main difference between the two is as follows:
▶ in an exponential decay relationship, the output values rapidly increase as
the value of the input increases.
▶ In exponential growth, the output increases in a considerablyrapid
manner as the input value increases.
5. Applications:-
Finance:
Natural growth and decay are also important
in financeparticularly in the calculation of compoundinterest.
Electrical circuits:
The Law of Natural Growth and Decay can also be used to model the
behavior of electrical circuits.
6. Radioactive decay:
The Law of Natural Growth and Decay is
commonly used to model the decay of radioactive isotopes
Chemical reactions:
Chemical engineers use the Law of Natural
Growth and Decay to model the
ratesofchemical reactions.
7. C O NCLUSIO N:-
▶ Overall, the Law of Natural Growth and Decay is a
powerful tool that can be used to model many different
types of systems in engineering.
