The carbon-14 activity of some ancient indian corn was found to be 7.0 disintegrations per minute (dpm) per gram of carbon. if present-day plant life has 16 dpm per gram of carbon, how old is the indian corn? (t1/2 = 5,730 yr)

6800 years old.  
First, let's determine the percentage of carbon-14 left. That will be simply 7.0 divided by 16, so 7.0/16 = 0.4375  
Now we need the base 2 logarithm to determine how many half-lives have expired, so: 
log(0.4375) / log(2) = -0.359021943 / 0.301029996 = 1.192645078  
So about 1.1926 half-lives have expired. Now multiply by the half-life of carbon-14. 
1.192645078 * 5730 = 6833.856297  
Rounding to 2 significant figures gives 6800 years.