the totla annual cost of health care in the united states grew from $993.3 billion in 1995 to $2151.1 billion in 2009 (statistical abstract of the united states.

1.find the average annual rate of growth r for the period by solving 2151.1=993.3(1 r)14

2.estimate the total annual cost of the health care in 2015 by reading the accompanying graph.

I think 1 shoud be 2151.1 = 993.3(1+r)^(14)

Please show us what you've attempted to solve this for r and we'll help you where you get stuck.

For (2) we can't see the graph, so can't help you.

2131.1/993.3=(1+ r)^14... divide by 993.3 to isolate the exponential portion

2.145474680358401 = (1 + r)^14... take the 14th root of both sides (N)^(1/14)

1.056039693532564 = 1 + r... subtract 1

0.056039693532564 = r... this is the rate as a decimal multiply by 100%

5.604% is the average rate of growth in health car costs.
is this right?

Yes - you have it right!

5.7%

2151.1=993.3 (1+r)14

2151.1 = 993.3 (1 + r)^14
divide both sides by 993.3
2.6561 = (1+r)^14
take ln (natural log) of both sides
0.7727 = 14 *ln (1+r)
Divide both sides by 14.
0.055192992 = ln (1+r)
take e of both sides
1.0567 = 1+r
so r = 0.0567 = 5.67%