Question

If 200 people have a cellular telephones in a company of 1000 employees. If the number of cellular phones was growing at 10% a year and the number of employees at 2% per year. How long will it take to have one cellular phone per employee? (assume continuous growth)

Answer 1

It will take 35 years for the number of cellular phones to double and for the number of employees to double. At that point, there will be one cellular phone per employee in the company.

Step-by-step explanation:

To find out how long it will take to have one cellular phone per employee, we need to determine the growth rates of both the number of cellular phones and the number of employees over time. Let's use the rule of 70 to calculate the time it will take for the number of cellular phones to double. The rule of 70 states that the time it takes for a quantity to double is equal to 70 divided by the growth rate as a percentage.

In this case, the growth rate is 10% per year. So, the time it takes for the number of cellular phones to double is 70 ÷ 10 = 7 years. Therefore, it will take 7 years for the number of cellular phones to grow from 200 to 400.

Next, let's calculate the time it will take for the number of employees to double. The growth rate for the number of employees is 2% per year. Using the rule of 70, we can calculate the time it takes for the number of employees to double as 70 ÷ 2 = 35 years.

Now, we need to find the common multiple of 7 years and 35 years, which represents the time it will take for both the number of cellular phones and the number of employees to double. The common multiple of 7 and 35 is 35 years.

Therefore, it will take 35 years for the number of cellular phones to double from 200 to 400, and for the number of employees to double from 1000 to 2000. At that point, there will be one cellular phone per employee in the company.