Distinguish exponential growth (b > 1) from decay (0 < b < 1)
Identify the initial value a, base b, and horizontal asymptote
Calculate doubling time and half-life
Compare growth rates across different bases
Key Equations
\( f(x) = a \cdot b^x \)
\( \text{Growth: } b > 1 \)
\( \text{Decay: } 0 < b < 1 \)
\( t_{double} = \frac{\ln 2}{\ln b} \)
\( t_{half} = \frac{\ln(0.5)}{\ln b} \)
Why It Matters
Exponential functions model population growth, radioactive decay, compound interest, and epidemic spread. Understanding the base parameter determines whether a quantity doubles or halves over time.