Answer: [tex]\bold{a)\quad g(x)=\bigg(\dfrac{1}{4}\bigg)\bigg5^{x-3}+2}[/tex]
Step-by-step explanation:
[tex]f(x)=a(5)^{b(x-c)}+d\\\bullet \text{a is a vertical stretch if }|a|>1\ \text{and a vertical compression if }|a|<1\\\bullet \text{b is a horizontal stretch (or compression)}\\\bullet \text{c is the horizontal shift to right (if positive) and left (if negative)}\\\bullet \text{d is the vertical shift up (if positive) and down (if negative)}[/tex]
Vertically compressed by one-fourth: a = [tex]\dfrac{1}{4}[/tex]
Shifted right three units: c = 3
Shifted up two units: d = 2
[tex]\large\boxed{g(x)=\bigg(\dfrac{1}{4}\bigg)\bigg5^{x-3}+2}[/tex]
