Your industry currently employs 3,800,000 workers. If this labor force is growing expotentially at an annual rate of 2.3% how long will it be before the number of employees reaches 5,000,000?
To calculate the time it will take for the number of employees to reach 5,000,000, we need to use the exponential growth formula:
P = P₀ * (1 + r)^t
Where:
P is the final population (5,000,000)
P₀ is the initial population (3,800,000)
r is the annual growth rate (2.3% or 0.023)
t is the time in years (what we need to find)
Rearranging the formula to solve for t, we have:
t = log(P / P₀) / log(1 + r)
Now let's substitute the values into the formula and solve for t:
t = log(5,000,000 / 3,800,000) / log(1 + 0.023)
Using a calculator, we can calculate:
t ≈ log(1.3158) / log(1.023) ≈ 9.14
So it will take approximately 9.14 years for the number of employees to reach 5,000,000 given an exponential growth rate of 2.3% per year.