Answer: [tex]\bold{b)\quad g(x)=\bigg(\dfrac{1}{2}\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-half: a = [tex]\dfrac{1}{2}[/tex]
Shifted left three units: c = -3
Shifted down two units: d = -2
[tex]g(x)=\bigg(\dfrac{1}{2}\bigg)\bigg5^{x-(-3)}-2[/tex]
[tex]\large\boxed{g(x)=\bigg(\dfrac{1}{2}\bigg)\bigg5^{x+3}-2}[/tex]
