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:
[tex]p = w \times 2^{\frac{x}{t}}[/tex]
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:
[tex]10.19 = 6.80 \times 2^{\frac{x}{7}}[/tex]
Divide both sides by 6.80
[tex]1.50 = 2^{\frac{x}{7}}[/tex]
Take the logarithm of both sides
[tex]\log(1.50) = \log(2^{\frac{x}{7}})[/tex]
Apply the law of logarithm
[tex]\log(1.50) = \frac{x}{7}}\log(2)[/tex]
Multiply both sides by 7
[tex]7 \times \log(1.50) = x\log(2)[/tex]
Divide both sides by log(2)
[tex]x = 7 \times \log(1.50) \div \log(2)[/tex]
[tex]x = 4.09[/tex]
Approximate
[tex]x \approx 4[/tex]
Hence, the doubling time is 4 years
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