6. dN A chemical substance has a decay rate of 9.2% per day. The rate of change of an amount N of the chemical after t days is given by - = - 0.092N. a) Let No represent the amount of the substance present at t = 0. Find the exponential function that models the decay. b) Suppose that 600 g of the substance is present at t = 0. How much will remain after 6 days? c) What is the rate of change of the amount of the substance after 6 days? d) After how many days will half of the original 600 g of the substance remain? a) N(t) = b) After 6 days, g will remain. Round to the nearest whole number as needed.) c) After 6 days, the rate of change is g/day. (Round to one decimal place as needed.) d) Half of the substance will remain after days. (Round to one decimal place as needed.) Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A, after time t. b) It is found that 18 lb of A will reduce to 9 lb in 4.1 hr. After how long will there be only 1 lb left? a) Choose the equation that gives A in terms of A,, t, and k, where k > 0. O A. A(1) = Akt OB. A(t) = Apekt O C. A(1) = App - kt O D. A(t) = A - kt b) There will be 1 lb left after hr. (Do not round until the final answer. Then round to the nearest whole number as needed.) 8. The half-life, T, for a particular radioactive element is 14 min. Find the decay rate of the element. The decay rate is * per min. (Do not round until the final answer. Then round to the nearest tenth as needed.) The decay rate, k, for a particular radioactive element is 1.9%, where time is measured in years. Find the half-life of the element. The half-life is years. (Round to one decimal place as needed.) 10. Of an initial amount of 7000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a rate of 3.15%/yr. 9 (Round to one decimal place as needed.) 11. The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t) = P, e - 0.000120971. How old is an ivory tusk that has lost 20 its carbon-14? The ivory tusk is years old. (Round to the nearest integer as needed.) 12. How much money must you invest now at 4.4% interest compounded continuously in order to have $10,000 at the end of 5 years? You must invest $ (Round to the nearest cent as needed.) 13. Find the present value of $7000 payable at the end of 2 years, if money may be invested at 8% with interest compounded continuously. The present value of $7000 is $ (Round to the nearest cent as needed.)