Hello I need some help with this question. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

11. Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using this known piece of information, scientists can date objects such as the Dead Sea Scrolls. (5 marks) The function N(t) = Noe-At represents the exponential decay of a radioactive substance. Nis the amount remaining after time t in years, No is the initial amount of the substance and 1 is the decay constant. (1 = 1.21 x 104) a) If the percentage of carbon-14 atoms remaining in a sample is 75%, how old is the sample? b) Find the rate of change of an initial amount of 1 gm of Carbon-14 found in the scrolls, if the decay constant is given as 1 = 1.21 x 104