Question

Solve the following word problems. 8. Professor Plum is concerned about his retirement He found a bank account that was paying 3.75% interest compounded annually. a. If he put $50,000 in the account, how long will it take for his account to be worth $100,000? b. If the same amount was compounding continuously, how much quicker would he get to $100,000? 9. Radioactive Cantstopdancium decays according to the following formula: y = aekt. a. The half-life of Cantstopdancium is 15 days. Use this information to calculate the k value for radioactive Cantstopdancium. Round k to 7 places. b. Use your k value in a formula to predict the amount that will be left after 20 days if the initial amount of Radioactive Cantstopdancium is 30 grams.

Answer 1

Ques 8=) part a.) solution: here we cese formula A= P ite where A is final amount Pis initial amount t is time and le is deate. = P = $ 50,00D , le = 3.75.1. = 0.0375 A = $ 100,000 $ 100,000 and and n= 1 of compounded & n = - 1 Annually J we have to find time to T y A= p lt r 75 o 50,000 TH 0-03757 T 100,000 = P 100000 = [1-0375] T 5oooo =2 = C1-03 75] Now we take Natweal

In 2 = ln C1.03757 € y ena= tx en 11.0375) en a = & ln (2) = 0.693 0.693= tx 0.068 ln (1.0375)=0.0368 0.693 =t 0.0368 time t = 118.8 3 yeares ] coves (b) solution! for compounding continually we - use the formala P = Poeet wheree P is findl amount Po is initial amount ris rate het is time = Po = $ 501000 , P = $100,000 r = 3.75.1. = 0.0375 P = Poert 0. 075 Xt = 501000 e & 1oo1000

looooo 0.0375 Xt - e. 5oooo 2 = 0.0 375xt » Now we take natural log both sides ln (2) = ln [ 200375 xt] - In 12) = 0.03758 t x line 0-693 = 0.0 375xx 1 4812) = 0.6934 ene = 1 » 0-693 at 0.0375 caves. y time (t) = (18.48 y eares