Find the 20th term of the geometric sequence when A1=2 and r=2
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Answer:
Step-by-step explanation:
Use the half life formula
where N is the amount after decay, No is the initial amount, e is Euler's number, k is the decay constant, and t is the time in minutes. For us, the first equation looks like this:
and we will solve that for k and then use that value of k in the second equation to find time.
Begin by dividing 7 by 12 to get
Now take the natural log of both sides since the natural log and that e are inverses. The e then disappears:
Plug the left side into your calculator and then set it equal to the right side, giving us:
Divide both sides by 70 to get the k value of
k = -.00769995
Now the second equation looks like this:
where t is our only unknown now that we know k.
Begin by dividing both sides by 12 to get
and take the natural log of both sides again to eliminate the e:
Take care of the left side on your calculator to get
-1.791759469 = -.00769995t and divide both sides by -.00769995 to get
t = 232.697 minutes