Question

A radiology specialist uses the radioactive substance​ iodine-131 to diagnose conditions of the thyroid gland. His hospital currently has a 24​-gram supply of​ iodine-131. The following table gives the number of grams remaining after a specified number of days.
t​ (Number of Days Starting from A 24​-Gram Supply of​ Iodine-131)
0
1
2
3
4
5
6
​N, Number of Grams of​ Iodine-131 Remaining from A​ 20-Gram Supply
24.00
22.39
20.89
18.19
16.97
16.97
15.83

Answer 1

c. Write an exponential decay formula for​ N, the number of grams of​ iodine-131 remaining, in terms of​ t, the number of days from the current supply of 24 grams.
The formula is N=
​(Use integers or decimals for any numbers in the​ expression.)
d. Determine the number of grams of​ iodine-131 remaining from a 24​-gram supply after 22 months ​(60 ​days).
N≈
​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

Answer 2

How long will it take for​ iodine-131 to decrease to half its original​ value?
It will take about _______days for​ iodine-131 to to decrease to half its original value.
​(Round to the nearest integer as​ needed)
Explain how to determine the answer in part f graphically.

Answer 3

General Equation is Amount remaining = Starting Amount * (Decay Rate) ^ t. Solve for the Decay rate by plugging in two points to solve or basically it is the later value divided by the earlier value of two consecutive readings.

Answer 4

Here are 4 half-life formulas and here is a link to half-life calculations:
http://www.1728.org/halflife.htm

Answer 5

Use this equation:
remaining amount or ending amount = beginning amount / 2^n
where n= number of half-lives
n = elapsed time/half-life
Note: the half-life of Iodine 131 is 8.0197 days
https://en.wikipedia.org/wiki/Iodine-131

Let's calculate after 1 day

remaining amount = 24/ 2^n
where n = 1/8.0197
remaining amount = 24/2^(1/8.0197)
remaining amount = 24/2^0.1246929436
remaining amount = 24/1.0902756589
remaining amount after 1 day= 22.0127816345 grams