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Exponential Function
High School
Definition
A function where the base is a positive constant and the exponent is the variable.
Formulas
f(x) = a^x (a > 0, a ≠ 1)
Definition of exponential function
a^x+y = a^x · a^y
Exponent rule
e^x = ∑_n=0^∈fty (xⁿ)/(n!)
Series expansion of natural exponential
Examples
Example 1
Solve 2^x = 32.
Example 2
Describe the graph of y = 3^x.
Applications
Biology
Cell division, population growth
Finance
Compound interest
Physics
Radioactive decay
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