Question

The annual health care costs for two new companies that opened in the year 2000 are shown on the graphs below.

Compare the average yearly increases in health care costs for both companies over the first 12 years.

Over the first 12 years, the average yearly increase in health care costs for company 1 is greater than the average yearly increase in health care costs for company 2 by about $750.

Over the first 12 years, the average yearly increase in health care costs for company 1 is greater than the average yearly increase in health care costs for company 2 by about $800.

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 $800.

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.

Answer 1

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.

Answer 2

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.