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2.) The average hourly wage *h(x)* of workers in an industry is modeled by the function *h(x)* = ,

where *x* represents the number of years since 1970.

a.) What does *x* represent?

b.) What does *h(x)* represent?

c.) What hourly wage does the model predict workers will make in the year 1993? Round your answer

to the *nearest dollar.*

d.) In what year does the model predict that wages will be $25 per hour?

GAMEMASTERX40 Feb 3, 2019

#1**+3 **

The average hourly wage h(x) of workers in an industry is modeled by the function where \(h(x)=\frac{16.24x}{0.062x+39.42}\) x represents the number of years since 1970.

a) *x *represents the number of years since 1970.

b) *h(x)* represents [t]he average hourly wage ... of workers

c) This question asks for *h(x) *given an input *x*.

Since *x *represents the number of years since 1970, we will have to find the number of years that have elapsed by using subtraction.

\(x=1993-1970=23\text{ years}\)

Now, let's find *h(x)*:

\(x=23\\ h(x)=\frac{16.24x}{0.062x+39.42}\) | This is the model of the hourly wage. |

\(h(23)=\frac{16.24*23}{0.062*23+39.42}\\\ h(23)=9.14459188...\approx\$9\) | I inputted the number of years and rounded appropriately to the nearest dollar |

d)

Since [t]he average hourly wage ... of workers is assumed to be $25, *h**(x)* =25, and we are solving for *x:*

\(h(x)=25\\ h(x)=\frac{16.24x}{0.062x+39.42}\) | Substitute in 25 for h(x) |

\(25=\frac{16.24x}{0.062x+39.42}\\ 25(0.062x+39.42)=16.24x\\ 1.55x+985.5=16.24x\\ 985.5=14.69x\\ x=\frac{985.5}{14.69}\approx 67.09\text{ years} \) | Solve for x by multiplying by the LCD, 0.062x+39.42 |

67 years after 1970 certainly lands in 2037, but the extra 0.09 years would fall into the following year, so the hourly wage will hit $25 per hour in 2038.

TheXSquaredFactor Feb 3, 2019