Question

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.

Answer 1

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
Answer:
the amount of time after which he will be earning $ 10.00 per hour is:
t = 6 years