★ Must-know
📌 For with a>0, the function represents exponential growth when b>1 and exponential decay when 0<b<1.
Further detail
📌 When b=1, is constant rather than exponential growth or decay, and a negative base does not produce a real-valued function for every real x.
Growth has b > 1, whereas decay has 0 < b < 1.
1. Which expression defines an exponential function in which the variable appears as an exponent?
2. What is the general form of an exponential function?
3. For , which condition on the positive base indicates exponential decay?
What is the form of an exponential function?
An exponential function has the form with positive base .
Exponential function symbol
f(x)=b^x, with b > 0
When does represent exponential growth?
It represents exponential growth when and .
Growth condition on b
b > 1 for growth, 0<b<1 for decay
What is the domain of the graph of ?
All real numbers.
Graph of f(x)=2^x
Domain all reals; y-intercept (0,1); asymptote y=0
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