Answer:
The amount of time after which he will be earning $10.00 per hour is 11.9 years.
Step-by-step explanation:
Given : Suppose that a new employee starts working at $7.03 per hour and receives a 3% raise each year. After time t, in years, his hourly wage is given by the equation [tex]y=\$7.03(1.03)^t[/tex].
To find : The amount of time after which he will be earning $10.00 per hour ?
Solution :
The equation is [tex]y=\$7.03(1.03)^t[/tex].
The amount of time after which he will be earning $10.00 per hour.
i.e. y=$10
Substitute in the equation and solve,
[tex]10=7.03(1.03)^t[/tex]
[tex]\frac{10}{7.03}=(1.03)^t[/tex]
Taking log both side,
[tex]\log (\frac{10}{7.03})=t\log (1.03)[/tex]
[tex]t=\frac{\log (\frac{10}{7.03})}{\log 1.03}[/tex]
[tex]t=11.9[/tex]
Therefore, the amount of time after which he will be earning $10.00 per hour is 11.9 years.
