Exponential function

In mathematics, an exponential function is a function of the form

The input variable x occurs as an exponent – hence the name. A function of the form f(x) = b^{x ± c} is also considered an exponential function, and a function of the form f(x) = a·b^x can be re-written as f(x) = b^{x ± c} by the use of logarithms and so is an exponential function.

In contexts where the base b is not specified, especially in more theoretical contexts, the term exponential function is almost always understood to mean the natural exponential function

also written as

where e is Euler's number, a transcendental number approximately 7000271828182800000♠2.718281828. The reason this number e is considered the "natural" base of exponential functions is that this function is its own derivative. Every exponential function is directly proportional to its own derivative, but only when the base is e does the constant of proportionality equal 1.

The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x), especially when it is impractical to write the independent variable as a superscript. The exponential function is widely used in physics, chemistry, engineering, mathematical biology, economics and mathematics.

EX

EX or Ex may refer to:

Relationships

Computing

Film and television

Mathematics

Music

Albums

Songs

Other uses

Expected value

In probability theory, the expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents. For example, the expected value of a six-sided die roll is 3.5 because, roughly speaking, the average of an extremely large number of die rolls is practically always nearly equal to 3.5. Less roughly, the law of large numbers guarantees that the arithmetic mean of the values almost surely converges to the expected value as the number of repetitions goes to infinity. The expected value is also known as the expectation, mathematical expectation, EV, average, mean value, mean, or first moment.

More practically, the expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value. The same works for continuous random variables, except the sum is replaced by an integral and the probabilities by probability densities. The formal definition subsumes both of these and also works for distributions which are neither discrete nor continuous: the expected value of a random variable is the integral of the random variable with respect to its probability measure.

S.E.X.

"S.E.X." is the first single by Lyfe Jennings from his second album The Phoenix. The song is about young teens losing their virginity from pressure. The song features R&B singer Yolanda "La La" Brown.

"S.E.X." debuted on the Billboard Hot 100 chart at number 99 and slipped off just to re-enter the following week again at number 99. It eventually peaked at number 37, making it Lyfe's (and Lala's) most successful single. "S.E.X." was a top-five hit on the Billboard Hot R&B/Hip-Hop Songs chart and received strong airplay on BET and some airplay on radio and MTV.

References

External links

Rebel Heart (Madonna album)

Rebel Heart is the thirteenth studio album by American singer and songwriter Madonna. It was released on March 6, 2015, by Interscope Records. Following the completion of the MDNA era, Madonna worked on the album throughout 2014, co-writing and co-producing it with various musicians, including Diplo, Avicii, and Kanye West. She teased by uploading pictures of her recording sessions on her Instagram account. Working with a number of collaborators posed problem for Madonna in keeping a cohesive sound and direction for Rebel Heart, unlike her previous efforts where only a few people were involved.

Thematically Rebel Heart represents the two different sides of the singer, her romantic and her rebellious side. The themes grew organically during the writing and recording sessions. Musically, it is a pop record which merges an array of genres such as 1990s house, trap and reggae, as well as the usage of acoustic guitars and gospel choir. Some of the songs are autobiographical in nature while others talk about love and introspection of Madonna's career. Rebel Heart features guest appearances from boxer Mike Tyson and rappers Nicki Minaj, Nas, and Chance the Rapper.