Exponential growth and Decay question

Question

Rewrite  $y=0.9^{t\ +\ 2}$y=0.9t + 2​ in the form $y=a(1+r)^t$y=a(1+r)t​ or $y=a(1-r)^t$y=a(1−r)t​ . Then tell whether the model represents exponential growth or exponential decay.

Answer 1

y = 0.9^t+2 = 0.9^t · 0.9² = (0.81)·(0.9)^t = (0.81)(1-0.1)^t where a = 0.81 and r = 0.1. This is exponential decay since 0.9 < 1.