00:01
In this question we have given a quantity of a substance decreased by 6 % in 9 hours and we have to find half life of a substance.
00:19
Let q of t be the quantity of substance after time.
00:39
Hence, quantity of substance at t is equal to 9 r is equal to 100 % minus 6 % multiplied with initial quantity, which implies quantity of substance as t is equal to 9 is equal to 94 % of q0.
01:03
It implies quantity at t is equal to 9 equals to 0 .94 q0.
01:11
Now using exponential decay formula, we can write it as q of t is equals to q0 time e -res to the power minus kt, where k is decay constant.
01:30
T is time.
01:32
Here it is in r's.
01:34
Q0 is initial quantity and q of t is quantity at times t.
01:48
So using this equation we can write it as q of 9 is equals to q0 multiplied with minus k multiply with 9.
02:00
It implies from this equation 1 we can substitute the value of q of 9 that is 0 .94 times.
02:09
Q0 is equal to q0 multiplied with e to the power minus 9k.
02:16
It implies 0 .94 is equals to e to the power minus 9k.
02:23
Here q0 and q0 get cancelled out.
02:29
Now taking log on both the sides we have log of 0 .94 is equal to log of 0 .94 is equal to log of e -restri -power minus 9k it implies log of 0 .94 is equal to minus 9k since we know that lne is always 1 it implies minus 0 .0 .01 8 7 is equal to minus 9k so on simplifying it we get it as k is equal to 0 .0 .0 .0 .7 is equal to 0 .0 .7.
03:22
7 is equal to 5 .7.
03:22
So on simplifying it we get it as k is here we have rounded of this value to the four decimal please.
03:28
Now we have to find the half life...