Question

Given G(r)=(1/2)^2r, evaluate.

Please solve a, b, and c

Answer 1

`G(r)=\left( \cfrac{1}{2} \right)^(2r) \\\\[-0.35em] ~\dotfill\\\\ G(0)=\left( \cfrac{1}{2} \right)^(2(0))\implies G(0)=\left( \cfrac{1}{2} \right)^0\implies G(0)=1 \\\\[-0.35em] ~\dotfill`

`G\left( (3)/(2) \right)=\left( \cfrac{1}{2} \right)^{2\cdot (3)/(2)}\implies G\left( (3)/(2) \right)=\left( \cfrac{1}{2} \right)^3\implies G\left( (3)/(2) \right)=\cfrac{1^3}{2^3} \implies G\left( (3)/(2) \right)=\cfrac{1}{8} \\\\[-0.35em] ~\dotfill\\\\ G(-2)=\left( \cfrac{1}{2} \right)^(2(-2))\implies G(-2)=\left( \cfrac{1}{2} \right)^(-4)\implies G(-2)=\left( \cfrac{2}{1} \right)^(+4) \\\\\\ G(-2)=\cfrac{2^4}{1^4}\implies G(-2)=16`