Question

James has worked for the same company his entire life. His current income is $100,000 per year. When he was originally hired, he made $50,000 per year. The company has given James a consistent raise of 2 percent every year. How long has James been with the company? Question 32 options:

75 years
10 years
35 years
25 years
50 years

Answer 1

By setting up an exponential growth equation and solving for the number of periods using logarithms, we determine that James has been with the company for approximately 35 years.

Step-by-step explanation:

To determine how long James has been with the company given that his salary increased from $50,000 to $100,000 with a consistent raise of 2% per year, we can use the formula for exponential growth. The general formula is Final Amount = Initial Amount * (1 + Growth Rate)^Number of Periods. In this case, our Final Amount is $100,000, the Initial Amount is $50,000, and the Growth Rate is 2%, or 0.02 when expressed as a decimal.

We can set up the equation as follows:

1. $100,000 = $50,000 * (1 + 0.02)^n
2. 2 = (1 + 0.02)^n
3. 2 = 1.02^n

Now, to solve for n (the number of years), we'll take the logarithm of both sides:

1. log(2) = log(1.02^n)
2. log(2) = n * log(1.02)
3. n = log(2) / log(1.02)
4. n ≈ 35 years

Calculating this using a scientific calculator or logarithm tables gives us n ≈ 35, which means James has been with the company for approximately 35 years.

Answer 2

(C) 35 Years

Step-by-step explanation:

James Current Income = $100,000 per year.

His first Income = $50,000 per year.

James Income is raised by 2% each year, that means his income for the next year is 102% of the previous year.

We can solve this using the nth term of a geometric progression since we are dealing with percentage.

The nth term of a G.P. is given as:
`U_n=ar^(n-1)`

a=$50,000, r=102%=1.02,
`U_n=100000`

Therefore:

`100000=50000*1.02^(n-1)\\(100000)/(50000) =1.02^(n-1)\\2=1.02^(n-1)`

To solve for n, we change from index form to logarithm

`Log_(1.02) 2=n-1`

`(Log 2)/(Log 1.02) =n-1\\35=n-1\\n=36`

Excluding his first salary, James has been with the company for 35 years.