Question

A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?

Answer 1

Amount remaining = 32 / 2^(time in days / 5 days)

Days
     Mass
0  32.00
1  27.86
2  24.25
3  21.11
4  18.38
5  16.00
6  13.93
7  12.13
8  10.56
9  9.19
10  8.00
11  6.96
12  6.06
13  5.28
14  4.59
15  4.00
16  3.48
17  3.03
18  2.64
19  2.30
20  2.00
21  1.74
22  1.52
23  1.32
24  1.15
25  1.00

First Column - arithmetic sequence
Second Column - Logarithmic Decay sequence

Answer 2

Answer:

The sequence in the first column represents an arithmetic sequence.

and the sequence in second column represents an geometric sequence.

Step-by-step explanation:

We are given a information that:

A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram.

  Number of days---------------- Mass remaining  

             0 ------------------------------ 32 grams  

             5 ------------------------------- 16 grams  

             10 ------------------------------ 8 grams  

             15 ------------------------------- 4 grams  

             20 ------------------------------- 2 grams  

             25 -------------------------------- 1 gram  

Thus; after 25 days (5 half-lives), the sample isotope has decayed from 32 grams to 1 gram .

1st column increasing by factor of '5' each increment  i.e. it is an arithmetic sequence.

2nd column being 'halved' each increment (multiplied by factor of 0.5) i.e. it is an geometric sequence.