Question

Instructions Answer the questions posed in this homework. When you are finished, scan or take a picture of your work and turn the file into Canvas. Solve these growth and decay problems. Make sure you show your work. Problems 1. Suppose you put with 10 pounds of living algae in a shallow growth pond on May 15. If the rate of increase is 5%/day and you harvest on September 15 (123 days later), how many pounds would you expect to harvest? 2. If a Macy's balloon contains 10,000 liters of Helium and it has a leak that results in 2,500 liters lost in the first hour after the balloon was filled. How much Helium will remain 4.5 hours later when the parade ends? 3. The half-life of the radioactive super-material, Tanonium is 25 hours. a. What is the decay rate? b. If you start with 10 grams of Tanonium, how much will you have in 81 hours? c. How long until all of the Tanonium is gone? d. If you start with 27 grams of Tanonium, how many hours until you have only 5 grams left?

Answer 1

1) Answer total increase algse, I initial algare, Ao = 10 prosunda rate of increse 5%, per dong no. of days 123 days Anot 18x5X123 10p 61.5 pounds Therefore fatal amount of algas to harvest hot I 10 4615 = 71.5 pounds 2.) Answer volume of Helium ballron, V=10,000 litres leak = 2500 litres (hour time - 4.5 hours leakage in 4.5 hours occu = 4:57.2500 litres - 11250 litres but we have only 10,000 litres available Sherefore After 4.5 hown there will be no Helium present in balloon.

3.) Answer Given half life of Tanonium, top2= 25 hour know that half life of a pst order reaction, ty 0.693 where K= duay rate -- K = 0.693 0.693 = 0.027725' te (1 Initial amount , [Ao] = rog time, t = 81 hours. have In [A]=-kt + ln (Ao] for first order reaction. 25 we =) ln(A) eoors g ln (Al 0.02772481 + lom (10) lola ) = -2.2176 + 2.3026 0.085 [Als 0.085 = 1.089 Therefore we have in 8 hours 1.089 089g when all Tanonium is gone, ln [A] = 0 enCA]=-kt tlnCA.] -0.02772t + ln 10 int- 83.066 hours 0.02772 (C) enio [A] = 279 [At] =50 les 5 = 0.02712t + ln 27 ens-ln 27=-0.02772t t1-6864 =10.027726 t- 1.6869 - 60.81 hours 0-02772