Suppose that a new employee starts working at $7.47 per hour and receives a 5% raise each year. after time t, in years, his hourly wage is given by the equation y equals $ 7.47 left parenthesis 1.05 right parenthesis superscript t baseline . find the amount of time after which he will be earning $10.00 per hour.

For this case we have an equation of the form:
 y = 7.47 * (1.05) ^ t
 For y = 10 we have:
 10 = 7.47 * (1.05) ^ t
 From here, we clear the value of t.
 We have then:
 (1.05) ^ t = 10 / 7.47
 log1.05 ((1.05) ^ t) = log1.05 (10 / 7.47)
 t = log1.05 (10 / 7.47)
 t = 5.978461004
 Rounding off we have:
 t = 6 years
 
 the amount of time after which he will be earning $ 10.00 per hour is:
 t = 6 years