Answer:
(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: [tex]U_n=ar^{n-1}[/tex]
a=$50,000, r=102%=1.02, [tex]U_n=100000[/tex]
Therefore:
[tex]100000=50000*1.02^{n-1}\\\frac{100000}{50000} =1.02^{n-1}\\2=1.02^{n-1}[/tex]
To solve for n, we change from index form to logarithm
[tex]Log_{1.02} 2=n-1[/tex]
[tex]\frac{Log 2}{Log 1.02} =n-1\\35=n-1\\n=36[/tex]
Excluding his first salary, James has been with the company for 35 years.
