Question

The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage

Answer 1

The doubling time of the hourly wage of the workers is an illustration of an exponential function that has a rate of 2

The doubling time of the wage is 4 years

How to determine the doubling time

A doubling function is represented as:

$p = w \times 2^{\frac{x}{t}}$

Where:

• p represents the final amount i.e. p = 10.19
• w represents the initial amount i.e. w = 6.80
• t represents the duration i.e. t = 7
• x represents the doubling time

So, we have:

$10.19 = 6.80 \times 2^{\frac{x}{7}}$

Divide both sides by 6.80

$1.50 = 2^{\frac{x}{7}}$

Take the logarithm of both sides

$\log(1.50) = \log(2^{\frac{x}{7}})$

Apply the law of logarithm

$\log(1.50) = \frac{x}{7}}\log(2)$

Multiply both sides by 7

$7 \times \log(1.50) = x\log(2)$

Divide both sides by log(2)

$x = 7 \times \log(1.50) \div \log(2)$

$x = 4.09$

Approximate

$x \approx 4$

Hence, the doubling time is 4 years

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