Group 3Math PresentationLogs, Natural Logs, and antilogsSolving equations with an unknown in the exponentDecay calculation using half-life :Group 3Math PresentationLogs, Natural Logs, and antilogsSolving equations with an unknown in the exponentDecay calculation using half-life Lesha Mullin Ben Weisman Zenia Kuder Jose Nunez


Ch 1 Sec 14 - Logs, Natural Logs, and antilogs :Ch 1 Sec 14 - Logs, Natural Logs, and antilogs Using a scientific calculator, find the natural log (ln) of the following number. (Problem #14). 2800 My calculator like many others has a button that automatically gives me the (ln). My calculator unlike most calculator I must press the key before putting the number. 1. Press (ln) key. 2. Input the number 2800. 3. Press the equal key, the answer is 7.937374696. 4. Round the answer to 7.937.


Sec 15. Ch 1 – Solving equations with an unknown in the exponent :Sec 15. Ch 1 – Solving equations with an unknown in the exponent Problem #5 10.5 = (8.6)(e1.35x) Solution: 10.5 / 8.6 = e1.35x ln1.22 = lne1.35x 1.99 = 1.35x 1.99 / 1.35 = x X = 0.15


Solving equations with an unknown in the exponent. :Solving equations with an unknown in the exponent. Calculator CVS Scientific Calculator To find ln: Press ln key Press in number (eg 1.22) Press =


Ch 1 Sec 15 Solving equations with an unknown in the exponent. :Ch 1 Sec 15 Solving equations with an unknown in the exponent. Problem #6 110 = (12)(e^(0.443)(x/0.5)) Solve for x


Ch 1 Sec 15 Solving equations with an unknown in the exponent. :Ch 1 Sec 15 Solving equations with an unknown in the exponent. x = 2.5 Take ln of both sides, after dividing 12 by both sides, of the equation to isolate the (e^(0.443)(x/0.5)) component making ln (110/12)= ((0.443)(x/0.5)) TI-30X SOLAR, press 110/12 (=2.2), then LN. Then, multiply both sides by 0.5 which = 1.11. Finally, solve for x dividing 1.11 by 0.443 = 2.5.


Ch 1 Sec 15 – Decay calculation using half-life :Ch 1 Sec 15 – Decay calculation using half-life Problem #10 To resolve exercise 10 using the DATEXX DS-700-36 scientific calculator: 8.6=25e-(0.693)(20/x)=8.6/25=e-(0.693)(20/x)=0.344(ln)=-0.693(20/x) -1.067= -0.693(20/x)= x = -0.693 x 20/- 1.067= 13 To be able to find ln, just press ln and then the number that you are working with (ln 0.344 and the = key)


Ch. 5 Sec 1 – Decay calculation using half-life :Ch. 5 Sec 1 – Decay calculation using half-life Problem #2 TI201 has a half-life of 73.1 hours. If a multidose vial contains 12.8mCi at 9.00am, how many will it contain at 10.00am the following day? Solution: A= 12.8mCi x e-0.396 x (25hr/73.1hr) =12.8mCi x e-0.237 =12.8mCi x 0.790 = 10.1mCi


Decay calcution using half-life :Decay calcution using half-life Calculator CVS scientific To find e-0.693: Press SHIFT Press e Press – is number is neg. Press number Press =


Ch 4 Sec 1 - Decay calculation using half-life :Ch 4 Sec 1 - Decay calculation using half-life Problem # 3 A vial of Xe133 gas is calibrated at 22 mCi at 6:00 am on March 1. What is its activity at 6:00 pm on March 8? t1/2=5.24d


Ch 4 Sec 1 - Decay calculation using half-life :Ch 4 Sec 1 - Decay calculation using half-life Answer = 8.2 mCi At = Aoe^-0.693(t/t1/2) At= 22 mCi e^-0.693(7.5 days/5.24) On the TI-30X SOLAR, press 7.5/5.24, which equals 1.4. Next press x -0.693 (=-0.97). Next press 2nd LN (=0.38) and then press x 22, which = 8.2


CH 5 Sec 1 – Decay calculation using half-life :CH 5 Sec 1 – Decay calculation using half-life Exercise 1: using DATEXX DS-700-36 scientific calculator. The first thing you must know is the formula At = Aoe-(0.693x)(t / t ½ ) A vial of generator eluate contains 432mCi immediately following elution. How many mCi will remain 8 hours later? The half-life for Tc99m is 6.01 hours A= 432mCi X e –(0.693)( 8hr / 6.01 h ) Divide 8hr / 6.01hr = 1.331 Multiple 1.331 x -0.693 = -0.92246 Press the SHIFT key - ln key and the = sign = 0.3975 Now multiply 432mCi x 0.3975 = 171.7 Round the number and the answer will be 172mCi