SOLUTION: Hi, any chance I could get some help with this question? Thanks in advance! https://drive.google.com/file/d/1aP4pFGQqFN3nVsqZb0HjqpvFIz26JHwd/view?usp=sharing

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Question 1189652: Hi, any chance I could get some help with this question?
Thanks in advance!
https://drive.google.com/file/d/1aP4pFGQqFN3nVsqZb0HjqpvFIz26JHwd/view?usp=sharing
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Assume:
 the initial amount of sucralose in a can of Diet Coke with Splenda is 40 mg
the initial amount means time=0, the amount+=40mg
 the amount of sucralose in a person’s body decreases by 50% every 2 days
means decreases by 50% =50%2F100=1%2F2 every 2 days

a. Complete the table of values for the above information. (1 mark)
Time
(days).............................Remaining Amount of Sucralose (mg)
0...........................................40mg
2............................................20mg
4............................................10mg
6............................................0mg


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
table of values is: 

time(days)           remaining amount of sucralose(mg)
0                             40
2                             20
4                             10
6                             5
8                             2.5


formula is y = a * b^x
a is the initial value.
b is the base for the exponent.
x is the exponent.

from the table, you get 40 = 40 * b^0.
since b^0 is always equal to 1, you get 40 = 40 and b is still undefined.

from the table, you get 20 = 40 * b^2.
solve for b^2 to get:
b^2 = .5
solve for b to get:
b = .7071067812.
from the table, you get 10 = 40 * b^4.
solve for b^4 to get:
b^4 = .25
solve for b to get:
b = .25^(1/4) = .7071067812.

from the table, you get 5 = 40 * b^6.
solve for b^6 to get:
b^6 = 1/8
solve for b to get:
b = (1/8)^(1/6) = .7071067812.

this very much indicates that b = .7071067812.

your formula is y = 40 * (.7071067812) ^ x

note that sqrt(.5) = .7071067812.

you can graph this formula.
it looks like this:



your unrounded formula is:

y = 40 * .7071067812 ^ x

your rounded formula is:

y = 40 * .71 ^ x

your rate of decay is 50% every 2 days.

every day, the amount of sucralose in the body is .7071067812 times the amount in the previous day.

that's a loss of (1 - .7071067812) = .2928932188 * the amount of sucralose from the previous day.

on day 0 you have 40.
on day 1 you have .7071067812 * 40 = 28.28427125.
that's a loss of 40 - 28.28427125 = 11.71572875 sucralos.
that is 11.71572875 / 40 = a loss of .2928932188 = 29.28932188%.

the rounded rate of decay formula is:
y = 40 * .71 ^ x
every day, you have .71 * the amount of sucralose in your body that you had the previous day.

let me know if you have any questions.

theo