From the course: Assembling Calculus

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Exponentials

Exponentials

From the course: Assembling Calculus

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Exponentials

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- [Instructor] An exponential function has the property that instead of raising a variable like X to a power, we instead have the variable in the exponent. This means that functions can get bigger or smaller very fast as the exponent gets more positive or more negative. Exponential functions have some very useful features in calculus that make them incredibly valuable for modeling real systems. Earlier, we looked at the derivative of two to the X power and we saw the curve in its derivative look like scaled versions of each other. It turns out that a derivative of an exponential function and the function itself only differ by a constant multiplier. That means that the integral is only different by that multiplier two. That multiplier is just the natural log of the number, and that brings us to what's a natural log. - [Instructor 2] You're probably familiar with a logarithm base 10. A base 10 logarithm is the power of 10…

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