Answer:
12 years
Step-by-step explanation:
Exponential Growing
Some variables tend to grow in time following an exponential function. The general equation for y as a function of t is
[tex]y=b.r^{at}[/tex]
The case given in the question corresponds to the following function
[tex]\displaystyle y=7.17(1.03)^t[/tex]
We want to know the amount of time after which the function will be 10, or
[tex]\displaystyle 7.17(1.03)^t=10[/tex]
Rearranging
[tex]\displaystyle 1.03^t=\frac{10}{7.17}[/tex]
Solving for t
[tex]\displaystyle Ln1.03^t=Ln(\frac{10}{7.17})[/tex]
[tex]\displaystyle t.Ln1.03=Ln(\frac{10}{7.17})[/tex]
[tex]\displaystyle t=\frac{Ln(\frac{10}{7.17})}{Ln\ 1.03}[/tex]
[tex]\displaystyle \frac{0,3327}{0,02959}[/tex]
[tex]\displaystyle t=11.26\ years[/tex]
When t=11 years, the employee is not paid at $10 per hour yet. We must jump to the next integer value.
[tex]t=12\ years[/tex]
