8. A substance has a half life of 2.347 minutes. a. If the initial amount of the substance was 110.4 grams, how many half-lives will have passed
before the substance decays to 6.9 grams.
b. What is the total time of the decay?

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

Where is the final population

is the initial population

is the growth factor

is the time taken for the growth 'b'

is the amount of time

Here, we are given that:

= 6. 9 grams

= 110.4 grams

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 .

Putting the values in the formula, we get:

Therefore, the answer is:

4 half lives have passed.

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

From answer of part a.):

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.