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`        please explain exponential functions`
7 years ago

105 Points
```										Dear yazdan,
Exponential functions look somewhat similar to functions        you have seen before, in that they involve exponents, but there is a big difference, in that the        variable is now the power, rather than the base. Previously, you have dealt with such functions        as f(x) = x2,        where the variable x was the base and the number 2 was the power. In the case of exponentials, however, you will be dealing with functions such as g(x) = 2x,        where the base is the fixed number, and the power is the variable.
Let's look more closely at the function g(x)        = 2x.        To evaluate this function, we operate as usual, picking values of x,        plugging them in, and simplifying for the answers. But to evaluate 2x,        we need to remember how exponents work. In particular, we need to remember that negative        exponents mean "put the base on the        other side of the fraction line".
Exponential functions always have some positive        number other than 1 as the base. If you think about it, having a negative number (such as –2)        as the base wouldn't be very useful, since the even powers would give you positive answers (such        as "(–2)2 = 4")        and the odd powers would give you negative answers (such as "(–2)3 = –8"), and what would you even do with        the powers that aren't whole numbers? Also, having 0 or 1 as the base would be kind of dumb, since 0 and 1 to any power are just 0 and 1,        respectively; what would be the point? This is why exponentials always have something positive        and other than 1 as the base.
All the best.
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Suryakanth –IITB
```
7 years ago
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