Unit 4: Exponential Functions

Key words

• Exponential functionKey word · Unit 4Exponential functionA rule that multiplies by the same positive factor for equal input steps.Exactly: A function $f(x)=a{b}^x$, with $a\ne 0$, $b>0$ and $b\ne 1$.Mix-up alert: A 20 percent increase uses a factor of 1.20, not 0.20.See this in Key wordsClose meaning
• Rational exponentKey word · Unit 4Rational exponentA fractional power that combines a root with a power.Exactly: For $a>0$ and integers $m,n$ with $n>0$, $a^{m/n}=(\sqrt[n]{a}{)}^m$. Negative bases require additional real-domain restrictions.Mix-up alert: The denominator tells you the root; the numerator tells you the power.See this in Key wordsClose meaning
• Common base methodKey word · Unit 4Common base methodRewrite both sides as powers of the same base.Exactly: If $b>0$ and $b\ne 1$, then $b^u=b^v$ implies $u=v$.Mix-up alert: The method needs equal bases and an injective exponential function.See this in Key wordsClose meaning