Answer:
a.) 4 half lives have passed
b) 9.388 minutes
Step-by-step explanation:
Formula for exponential growth / decay is given as:
[tex]A=A_0b^{\frac{t}{c}}[/tex]
Where [tex]A[/tex] is the final population
[tex]A_0[/tex] is the initial population
[tex]b[/tex] is the growth factor
[tex]c[/tex] is the time taken for the growth 'b'
[tex]t[/tex] is the amount of time
Here, we are given that:
[tex]A[/tex] = 6. 9 grams
[tex]A_0[/tex] = 110.4 grams
[tex]b = \dfrac{1}{2}[/tex]
[tex]c = 2.347[/tex] min
To find:
a.) Number of half lives taken for the decay.
b.) Total time in the decay.
Solution:
a.) Number of half lives taken for the decay is nothing but equal to [tex]\frac{t}{c}[/tex].
Putting the values in the formula, we get:
[tex]6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4[/tex]
Therefore, the answer is:
4 half lives have passed.
b.) Total time of decay. We have to find the value of [tex]t[/tex] here.
From answer of part a.):
[tex]\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}[/tex]
