Suppose that a new employee starts working at ​$7.57 per​ hour, and receives a 3​% raise each year. After time​ t, in​ years, his hourly wage is given by the function P(t)=$7.57(1.03)t.

Question

Suppose that a new employee starts working at ​$7.57 per​ hour, and receives a 3​% raise each year. After time​ t, in​ years, his hourly wage is given by the function P(t)=$7.57(1.03)t.

​a) Find the amount of time after which he will be earning​ $10.00 per hour.

​b) Find the doubling time.After what amount of time will the employee be earning​ $10.00 per​ hour? __ years

Answer 1

10 = 7.57(1.03)^t

(1.03)^t = 10/7.57 = 1.321

t= about 9.42 years

in one year, $7.57 rate increases to 1.03(7.57) = 7.80

a 23 cent increase

in 10 years that's a minimum 2.30 raise,but the annual compounding makes it less time: 9.42 years

doubling time is when he earns 2 x 7.57= $15.14

15.14/7.57 = 2

(1.03)^t = 2

t =about 23.3 years to double the salary