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# 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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