a. Living matter (both human and non-human) absorbs carbon-14. When living matter dies, there is no longer absorption of carbon-14; and the amount of carbon-14 very slowly diminishes in a dead object. However much carbon-14 is present in a dead object, it takes 5730 years for carbon-14 to diminish to half its value (i.e., the half-life of carbon-14 is 5730 years). The equation relating the number of carbon-14 atoms at two points in time is, where t denotes time measured in years,denotes the number of atoms of Carbin-14 in an object when death occurs, andis the number of carbon-14 atoms t years later. [As an aside, and not needed to do this problem,is known because there is a relation between carbon-14 and carbon-12 (which does not deteriorate).] Find the yearly rate of decline rin carbon-14 atoms. You should get a negative number because

b. How old is an object that now has 10% of the carbon-14 atoms that it had when it died