Company 1:
Average yearly increases in health care costs for the Company 1 over the first 12 years is:
r1=[f(12)-f(0)]/(12-0)
r1=[f(12)-f(0)]/12
f(12)=(24,000+36,000)/2
f(12)=60,000/2
f(12)=30,000
f(0)=12,000
r1=(30,000-12,000)/12
r1=18,000/12
r1=1,500
Company 2:
Average yearly increases in health care costs for the Company 2 over the first 12 years is:
r2=[g(12)-g(0)]/(12-0)
r2=[g(12)-g(0)]/12
g(12)=(36,000+48,000)/2
g(12)=84,000/2
g(12)=42,000
g(0)=[12,000+(12,000+24,000)/2]/2
g(0)=(12,000+36,000/2)/2
g(0)=(12,000+18,000)/2
g(0)=30,000/2
g(0)=15,000
r2=(42,000-15,000)/12
r2=27,000/12
r2=2,250
r2=2,250>1,500=r1
r2-r1=2,250-1500
r2-r1=750
Answer: Fourth option:
Over the first 12 years, the average yearly increase in health care costs for company 2 is greater than the average yearly increase in health care costs for company 1 by about $750.
