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myrzilka [38]
3 years ago
5

8. A substance has a half life of 2.347 minutes.

Mathematics
1 answer:
mina [271]3 years ago
7 0

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

A=A_0b^{\frac{t}{c}}

Where A is the final population

A_0 is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, we are given that:

A = 6. 9 grams

A_0 = 110.4 grams

b = \dfrac{1}{2}

c = 2.347 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 \frac{t}{c}.

Putting the values in the formula, we get:

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

Therefore, the answer is:

<em>4 half lives </em>have passed.

b.) Total time of decay. We have to find the value of t here.

From answer of part a.):

\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}

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