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Some examples include:
* Growth of populations, under certain circumstances
* Radioactive decay
* In quantum physics, the probability of finding a particle at a specific point
* The temperature of an object, when it is allowed to cool down
* The charge on a capacitor which is allowed to discharge
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What is the difference between exponential functions and logarithmic functions?
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
What is the difference between power functions and exponential functions?
Power functions are functions of the form f(x) = ax^n, where a and n are constants and n is a real number. Exponential functions are functions of the form f(x) = a^x, where a is a constant and x is a real number. The key difference is that in power functions, the variable x is raised to a constant exponent, while in exponential functions, a constant base is raised to the variable x. Additionally, exponential functions grow at a faster rate compared to power functions as x increases.
Are exponential functions always concave up?
Yes.
How are exponential and logarithmic functions related?
They are inverses of each other.
How are linear and exponential functions alike?
They have infinite domains and are monotonic.
