Question

A new truck that sells for 29,000 depreciates 12% each year. What is the decay factor b?

Answer 1

$\bf y=a(b)^t\qquad or\qquad A=I(1-r)^t\qquad \textit{let's check}\\\\ -------------------------------\\\\ \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &29000\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=29000(1-0.12)^t\implies \begin{array}{llll} A=&29000(0.88)^t\\ &\uparrow \qquad\quad \uparrow \\ &a\qquad\quad b \end{array}$