Question

Suppose that a new employee starts working at ​$7.67 per hour and receives a 3​% raise each year. After time​ t, in​ years, his hourly wage is given by the equation .y=$7.67(1.03)t. Find the amount of time after which he will be earning​ $10.00 per hour.
After what amount of time will the employee be earning​ $10.00 per​ hour?

Answer 1

Answer:

  9 years

Step-by-step explanation:

You want to find t such that y=10.

  10 = 7.67(1.03)^t

  10/7.67 = 1.03^t . . . . . divide by 7.67

  log(10/7.67) = t·log(1.03) . . . . . . take logs

  log(10/7.67)/log(1.03) = t ≈ 8.9743 . . . . . years

After about 9 years, the employee will be earning $10 per hour.