1. If an investment of $7500 compounded continuously at 4% p.a. how much will this investment be worth in 5 years?
2. How many years would you have to invest $1000 in order to double your money if you where offered 2.5% /a interest compounded continuously ?
3. A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model
4. In 1991 a German man, Helmut Simon, discovered the frozen remains of a prehistoric man in an Alpine glacier while hiking along the border of Austria and Italy. Interest was generated around the world as people wondered who this "Iceman" was and how long he had been frozen in the glacier. Osti, as the prehistoric man was named, was found clothed in fur and leather and carried a spear-like weapon. a. Given that the C14 had decayed to 65.337% of its original mass,, use the carbon dating formula in Winplot to determine the approximate age of the prehistoric man. b. Using Desmos, set the domain from -500 to 10000 and range from -0.1 to 1. c. How could this desmos be used to demonstrate how any object could be dated given the percentage of C14 left undecayed?
5. Using the curve constructed for the decomposition of Carbon 14 above find the age of a prehistoric cave painting discovered in the Lascaux Caves in southern France if the amount of Carbon 14 has decayed to 40% of it's original mass.