Question

MATH 30 POINTS WILL GIVE BRAINLIEST help please

Answer 1

The fundamental behavior that's important here is that, as $t$ gets arbitrarily large, $a^t$ becomes smaller (decays) if $|a|$ and larger (grows) if $|a|>1$.

$100\left(1-\dfrac12\right)^t=100\left(\dfrac12\right)^t\implies\dfrac12$

$0.1(1.25)^t\implies1.25>1\implies\text{growth}$

$426(0.98)^t\implies0.98$

$2050\left(\dfrac12\right)^t\implies\text{decay}$

$\left((1-0.03)^{1/2}\right)^{2t}=0.97^t\implies0.97$