Answer:
a) Average hourly wage in 2016 is $13.98
b) In year 2006, the average hourly wage be $23.
Step-by-step explanation:
We are given the following in the question:
[tex]w(t) = 10.2e^{0.0315t}[/tex]
where t = 0 corresponds to 1990.
a) average hourly wage in 2000
For year 2000, we put t = 10
Putting the values, we get,
[tex]w(10) = 10.2e^{0.315}\\w(10) = 13.98\$[/tex]
Average hourly wage in 2000 is $13.98
b) year in which the average hourly wage be $23
Putting the values we get,
[tex]23 = 10.2e^{0.0315t}\\\\t = \displaystyle\frac{1}{0.0315}\ln \bigg(\frac{23}{10.2}\bigg)\\\\t = 25.81\approx 26[/tex]
Thus, in year 2016, the average hourly wage be $23.
