suppose that a new employee starts working at $7.54 per hour, and receives a 4% raise each year. After time t, in years, his hourly wage is given by the function P(t)=$7.54(1.04)^t.

Question

Fine the amount of time in which he will be earning $10.00 per hour.

Answer 1

P(t) = 7.54(1.04)^t

10 = 7.54(1.04)^t

1.325 ≈ 1.04^t

ln 1.325 = ln 1.04 t

0.281 ≈ 0.039 t

7.164 ≈ t

Answer 2

P(t)=$7.54(1.04)^t

$10.00=$7.54(1.04)^t

10/7.54=(1.04)^t

1.3262599=(1.04)^t

log(1.3262599)=log(1.04)^t

log(1.3262599)=t(log(1.04))

t=log(1.3262599)/log(1.04)

t=0.1226286388/0.0170333393

t=7.199 years

t≈7.2 years