Question

Please help me solve question

Answer 1

In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.

What we can find here first is the rate of the increase of the salary of the workers. We can use the equation

`y=y_0e^(rt)`

We are looking for the value of r. We have to derive an equation solving for r. We have

`\begin{gathered} \frac{y}{y_0^{}}=e^(rt) \\ rt=\ln (y)/(y_0) \\ r=(1)/(t)\ln (y)/(y_0) \end{gathered}`

Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get

`\begin{gathered} r=(1)/(15)\ln ((29.59)/(6.70)) \\ r=0.099yr^(-1) \end{gathered}`

The doubling time is computed as

`d=(\ln 2)/(r)`

Substitute the value of r on the equation above and solve, we get

`d=(\ln 2)/(0.099)=7.00yr`

Hence, the doubling time for this problem is equal to 7 years.

Answer: 7 years