Question

Suppose that a new employee starts working at ​$7.65 per hour and receives a 5​% raise each year. After time​ t, in​ years, his hourly wage is given by the equation y=$7.65(1.05)^t. Find the amount of time after which he will be earning​ $10.00 per hour.

Answer 1

The answer is:

5.49 years

but if you round it then it's:

5.5 years

Answer 2

5.49 years

Explanation:

y = $7.65(1.05)^t

You want to know for which value of t, y equals $10.

$10 = $7.65(1.05)^t

10/7.65 = 1.05^t

log (10/7.65) = log 1.05^t

log (10/7.65) = t(log 1.05)

t = [log(10/7.65)]/(log 1.05)

t = 5.49