2e^(2x)
Definition
2e^(2x) is an exponential function that represents the growth or decay of a quantity at a rate of 2 times the base of natural logarithm, e, raised to the power of 2x.
Analogy
Imagine you have a pet hamster named "e" and it multiplies really fast. Every time you blink your eyes (represented by x), the number of hamsters doubles because they grow at an exponential rate. So, if you blinked twice (2x), you would end up with 4 times as many hamsters (2e^(2x)).
Related terms
Exponential Function: A mathematical function where the variable appears in the exponent. It grows or decays rapidly depending on the value of its base.
Natural Logarithm (ln): The inverse function of exponential functions with base e. It gives us the exponent needed to obtain a certain value using e as the base.
Growth Rate: The rate at which a quantity increases over time. In this case, it is represented by 2 in front of e^(2x), indicating rapid growth.
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