★ 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. For , which condition on the positive base indicates exponential decay?
3. Which pair correctly gives the domain and range of ?
What is the form of an exponential function?
An exponential function has the form with positive base .
When does represent exponential growth?
It represents exponential growth when and .
What is the domain of the graph of ?
All real numbers.
How does behave as x approaches negative infinity?
It approaches 0.
Exponential function symbol
f(x)=b^x, with b > 0
Growth condition on b
b > 1 for growth, 0<b<1 for decay
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