# Applications of Exponential and Logarithmic Functions

Exponential and logarithmic functions are important algebraic functions with advanced applications, including the studies of citizenry growth, radioactive decay, and admixture interest. An exponential action has the anatomy f(x) = C * b^x, area b is a absolute connected accepted as a base, C is an approximate constant, usually positive, and the altercation x plays the role of an exponent. If b is greater than 1, again f(x) increases with x; contrarily it decreases with x. Even a almost baby abject after-effects in actual accelerated growth.

One archetype of an exponential action is admixture interest. For instance, an antecedent investment of $1000 with a 5% anniversary absorption bulk circuitous annually will abound according to the blueprint A(t) = 1000 * (1.05)^t, area t is the bulk of years the money has been invested. Such an investment will bifold almost every 14 years.

Another archetype of about exponential advance is population. A arena with a anchored citizenry advance bulk has a citizenry which grows according to the blueprint P(t) = P0 * (1 + r)^t, area P0 is the antecedent population, P(t) is the citizenry afterwards t years, and r is the anniversary citizenry advance rate. In February 2008, the apple citizenry was estimated at 6.65 billion, with an anniversary advance bulk of 1.17%. At that rate, the apple citizenry will ability 10.85 billion by 2050.

A third archetype of an exponential action is radioactive decay. The bulk of a radioactive actuality with a half-life of T_1/2 decays according to the blueprint N(t) = N(0) * 2^(-t/T_1/2). Radioactive isotopes are acclimated to actuate the ages of fossils as able-bodied as age-old artifacts by agency of this formula.

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