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# Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N. 1) displaystyle{y}={0.8}^{x} 2) displaystyle{y}=-{3}{x}-{8} 3) displaystyle g{{left({x}right)}}={left(frac{1}{{2}}right)}^{x} # Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N. 1) displaystyle{y}={0.8}^{x} 2) displaystyle{y}=-{3}{x}-{8} 3) displaystyle g{{left({x}right)}}={left(frac{1}{{2}}right)}^{x}

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Modeling asked 2020-11-05
Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N.
1) $$\displaystyle{y}={0.8}^{x}$$
2) $$\displaystyle{y}=-{3}{x}-{8}$$
3) $$\displaystyle g{{\left({x}\right)}}={\left(\frac{1}{{2}}\right)}^{x}$$

## Answers (1) 2020-11-06
Given, 1) $$\displaystyle{y}={0.8}^{x}$$
2) $$\displaystyle{y}=-{3}{x}-{8}$$
3) $$\displaystyle g{{\left({x}\right)}}={\left(\frac{1}{{2}}\right)}^{x}$$
we have to find decay factor
Here 1) $$\displaystyle{y}={0.8}^{x}$$ which is exponential function of the form of
$$\displaystyle{y}={a}{\left({b}\right)}^{x}\text{where}\ {a}={1},{b}={0.8}$$
Hence, the decay factor is: 0.8
2) $$\displaystyle{y}=-{3}{x}-{8},$$ Decay factor is N
3) $$\displaystyle g{{\left({x}\right)}}={\left(\frac{1}{{2}}\right)}{x},$$
Decay factor is $$\displaystyle\frac{1}{{2}}$$

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