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?
Each year the workers are 2.3% more than the year before. Thus, each year the workforce is 1.023 as big as it was before.
After x years, the workforce is
380000*1.023x
so, to find how many years to get to 5000000, solve
380000*1.023x = 5000000
1.023x = 50/38 = 1.316
x ln 1.023 = ln 1.316
x = 12.076 years