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

Answer:

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

Step-by-step 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,

$10=7.03(1.03)^t$

$\frac{10}{7.03}=(1.03)^t$

Taking log both side,

$\log (\frac{10}{7.03})=t\log (1.03)$

$t=\frac{\log (\frac{10}{7.03})}{\log 1.03}$

$t=11.9$

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

Answer 2

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