Question

suppose that a new employee starts working at $7.03 per hour and receives a 3% raise each year. After time t, in years, his hourly wage is given by the equation y=$7.03(1.03)^t. find the amount of time after which he will be earning $10.00 per hour.

Answer 1

Solve the following: $10 = $7.03(1.03)^t for t.

log 10 - log 7.03 = tlog 1.03. Solve for t.

1 - 0.847
---------------- = t = 11.77 years (answer)
0.013

Answer 2

The amount of time after which he will be earning $10.00 per hour is 11.9 years.

Explanation:

Given : Suppose that a new employee starts working at $7.03 per hour and receives a 3% raise each year. After time t, in years, his hourly wage is given by the equation
`y=\$7.03(1.03)^t`.

To find : The amount of time after which he will be earning $10.00 per hour ?

Solution :

The equation is
`y=\$7.03(1.03)^t`.

The amount of time after which he will be earning $10.00 per hour.

i.e. y=$10

Substitute in the equation and solve,

`10=7.03(1.03)^t`

`(10)/(7.03)=(1.03)^t`

Taking log both side,

`\log ((10)/(7.03))=t\log (1.03)`

`t=(\log ((10)/(7.03)))/(\log 1.03)`

`t=11.9`

Therefore, the amount of time after which he will be earning $10.00 per hour is 11.9 years.