3MAN 3) All living organisms contain 1 part per trillion parts of a radioactive substance known as "carbon-14." Carbon-14 has a half-life of 5730 years after the organism dies. Knowing this allows archaeologists to date artefacts that they find. (a) Create an equation that represents the half-life of carbon-14 in organic artefacts. (b) How many parts per trillion of carbon-14 would be found in a piece of cloth that is 5730 years old? (c) How many parts per trillion of carbon-14 would be found in a 50,000 year old animal bone? (d) A map contains 0.9312 parts per trillion of carbon-14. In approximately what year was the map made? a ) fex) = 4) A town has a population of 8400 in 1990. Fifteen years later, its population grew to 12500. (a) Determine the average annual growth rate of the town's population. (b) Write an equation that represents the population growth of the town since 1990. (c) Determine the population this year. P (x ) = 8400