+73 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?
+2446 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.
