12. Find the effective rate corresponding to the following nominal rate. 8% compounded quarterly The effective rate is |%. (Round to the nearest hundredth as needed.) 13. Find the present value of the deposit. $43,000 at 5.9% compounded continuously for 5 years The present value is $ (Round to the nearest cent as needed.) 14. When an antibiotic is introduced into a culture of 90,000 bacteria, the number of bacteria decreases exponentially. After 5 hours, there are only 40,000 bacteria. a. Write an exponential equation to express the growth function y in terms of time t in hours. b. In how many hours will half the number of bacteria remain? a. The exponential equation is (Round to three decimal places as needed.) b. Half the number of bacteria will remain in hours. (Round to one decimal place as needed.) 15. The half-life of plutonium-241 is approximately 13 years. a. How much of a sample weighing 4 g will remain after 120 years? b. How much time is necessary for a sample weighing 4 g to decay to 0.1 g? a. After 120 years, g will remain. (Do not round until the final answer. Then round to four decimal places as needed.) b. The sample will decay to 0.1 g after years . (Do not round until the final answer. Then round to the nearest year.)