Title: 6_1 The Exponential Function
Course: HELM Workbooks 2023-2024 > Section: HELM 6: Exponential and Logarithmic Functions

In this quiz we revisit the use of exponents. We consider how the expression \( a^x\) is defined when \(a\) is a positive number and \(x\)  is irrational. Previously we have only considered examples in which \(x\) is a rational number. We consider these exponential functions \(f(x)=a^x\) in more depth and in particular consider the special case when the base \(a\) is the exponential constant \(e\) where: \[\qquad e = 2.7182818 \dots \] We then examine the behaviour of \( e^x\) as \(x\rightarrow\infty\), called exponential growth and of \( e^{-x}\) as \(x\rightarrow\infty\), called exponential decay.