The function f(x) with respect to x is given in the table :

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}{X}&-{2}&-{1}&{0}&{1}&{2}\backslash{h}{l}\in{e}{f{{\left({x}\right)}}}&{0.18}&{0.9}&{4.5}&{22.5}&{112.5}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

From the table it is shown that ,

The multiplier for every next coordinate is 5.

Therefore the common ratio formed is ,

\(\displaystyle{r}={\frac{{{0.9}}}{{{0.18}}}}\)

\(\displaystyle={5}\)

The initial value of the function is \(\displaystyle{a}={4.5}\)

The general form of the exponential form is,

\(\displaystyle{y}={a}\cdot{r}^{{x}}\)

Substitute the values,

\(\displaystyle{y}={4.5}{\left({5}\right)}^{{x}}\)

Thus the exponential function formed is \(\displaystyle{f{{\left({x}\right)}}}={y}={4.5}{\left({5}\right)}^{{x}}\)

The function g(x) with respect to x is given in the table :

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}{X}&-{2}&-{1}&{0}&{1}&{2}\backslash{h}{l}\in{e}{g{{\left({x}\right)}}}&{12}&{6}&{3}&{1.5}&{0.75}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

From the table it is shown that ,

The multiplier for every next coordinate is 0.5.

Therefore the common ratio formed is,

\(\displaystyle{r}={\frac{{{6}}}{{{12}}}}\)

\(\displaystyle={0.5}\)

The initial value of the function is 3.

The general form of the exponential form is,

\(\displaystyle{y}={a}\cdot{r}^{{x}}\)

Substitute the values,

\(\displaystyle{y}={3}{\left({0.5}\right)}^{{x}}\)

Thus the exponential function formed is \(\displaystyle{g{{\left({x}\right)}}}={3}{\left({0.5}\right)}^{{x}}\)

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}{X}&-{2}&-{1}&{0}&{1}&{2}\backslash{h}{l}\in{e}{f{{\left({x}\right)}}}&{0.18}&{0.9}&{4.5}&{22.5}&{112.5}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

From the table it is shown that ,

The multiplier for every next coordinate is 5.

Therefore the common ratio formed is ,

\(\displaystyle{r}={\frac{{{0.9}}}{{{0.18}}}}\)

\(\displaystyle={5}\)

The initial value of the function is \(\displaystyle{a}={4.5}\)

The general form of the exponential form is,

\(\displaystyle{y}={a}\cdot{r}^{{x}}\)

Substitute the values,

\(\displaystyle{y}={4.5}{\left({5}\right)}^{{x}}\)

Thus the exponential function formed is \(\displaystyle{f{{\left({x}\right)}}}={y}={4.5}{\left({5}\right)}^{{x}}\)

The function g(x) with respect to x is given in the table :

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}{X}&-{2}&-{1}&{0}&{1}&{2}\backslash{h}{l}\in{e}{g{{\left({x}\right)}}}&{12}&{6}&{3}&{1.5}&{0.75}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

From the table it is shown that ,

The multiplier for every next coordinate is 0.5.

Therefore the common ratio formed is,

\(\displaystyle{r}={\frac{{{6}}}{{{12}}}}\)

\(\displaystyle={0.5}\)

The initial value of the function is 3.

The general form of the exponential form is,

\(\displaystyle{y}={a}\cdot{r}^{{x}}\)

Substitute the values,

\(\displaystyle{y}={3}{\left({0.5}\right)}^{{x}}\)

Thus the exponential function formed is \(\displaystyle{g{{\left({x}\right)}}}={3}{\left({0.5}\right)}^{{x}}\)