Important When answering questions in a mathematics course, always use the following guidelines to help you do your best: 0 Provide full solutions, showing all of your steps. 0 Make sure that there is one step or idea per line. 0 Use one equal sign per line. 0 Make sure that equal signs line up vertically. 0 Don't use selfdeveloped short form notations. 0 Make sure all graphs are titled with labeled axes 3. The plutonium isotope Pu-239 is a radioactive material. The half-life of plutonium isotope Pu-239 is 24 360 years. Ten grams of plutonium is released in a nuclear accident. (4 marks each) a. Determine the rule, domain, and range of the function model. b. How long will it take for the 10 grams to decay to 1 gram? Round off your answer to the nearest year. 4. A bacteria culture population of 50 bacteria doubles in size every 20 minutes. (4 marks each) a. Establish the function rule that models this situation and graph it. b. How long will it take for the bacterial culture grow to a population of 250 000? 5. The temperature of a cooling liquid over time can be modeled by the exponential function T013) 2 60(%) m l 20, where T012) is the temperature in degrees Celsius, and a: is the elapsed time in minutes. a. Graph the function and determine how long it takes for the temperature to reach 28 c'C. (5 marks) b. What was the initial temperature? (2 marks) 6. The initial dryweight of Botryococcus braunii, a green microalgea, is 50 mg/L. Under the right conditions of light, temperature, salinity and ph, the algea triples every three hours for the first 15 hours of growth. (3 marks each) a. Determine the rule, domain, and range of the function model. b. Graph the function model