alleryStart learning →Why is the base of an exponential function never allowed to be 1?
AIt would give a negative rule
BIt would give no y-intercept
CIt would give a constant rule
DIt would give a linear rule
Answer & Solution
Correct answer: C. It would give a constant rule
1. An exponential function raises a fixed base to a variable power.
2. The number 1 raised to any power is still 1.
3. So a base of 1 would produce the same output for every input, which is a constant rule.
4. A constant rule has none of the growth or decay behaviour that exponential functions are used for.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.2 Evaluate and Graph Exponential Functions_
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