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}

Question
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 \(\displaystyle\frac{1}{{2}}\)
0

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