Question

For pre-calc i don't understand how the t values were determined in the following problem:
A certain radioactive isotope has a half-life of 11 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?
t=0 is 32 grams
t=5 is 16 grams
t=10 is 8 grams
t=15 is 4 grams
t=20 is 2 grams and
t=25 is 1 gram

Answer 1

so if anyone could explain that would be great. thank you!

Answer 2

If I understand the question correctly, we are ask to describe the sequence used in the first column and as well as the second column. The first column follows an arithmetic sequence while first second is a geometric sequence.

Answer 3

The common difference between each t value is 5, while the common ratio between each mass value is 1/2.

Answer 4

how do you know that the t values go by fives? I understand the sequences but I need the actual t value explained because those columns are the answers

Answer 5

The only way to get from 0 to 5 is to add 5 to 0. We can observe that the step between each t value is 5. For example, 5 - 0 = 5, 10 - 5 = 5, 15 - 10 = 5, and so on. Does this answer your question?

Answer 6

Every 11 days, the amount of that radioactive materials is reduced by half.
So at time zero amount = 32 grams.
Continuing with this progression:
Time (days) Amount
11 16
22 8
33 4
44 2
55 1

The equation for this would be
Amount = Orig Amount * 1/ ((2 ^ (days / 11))
Amount = 32 * 1 / (2 ^ days / 11)

A good calculator and a good explanation of this can be found here:
http://www.1728.org/halflife.htm

Answer 7

Yes, like the 2 of you, I have NO idea why those time values were chosen.
Maybe you are to calculate the time values by
t(1) = 5 * 2.2
t(2) = 10 * 2.2
t(3) = 15 * 2.2
and so on.

Answer 8

Yes, I'm not sure why there is a step of 5 if the period would be every eleven days. However, the question seems to be asking us to state the type of sequence used in each column of data.

Answer 9

i know what types of sequences i was just wondering why t is moving on intervals of 5

Answer 10

OR maybe it was added just to make a complex problem even more complicated.
I guess they want you to "understand" that for this (or any other problem) you must find some value k (or 2.2) such that it will fit the right side of the equation.

Maybe it is something like time = distance / velocity.

So, we could say that
As the time doubles, the distance traveled will double.

In this "table" we could say

dist velocity
0 0
1 1
2 2
3 3
4 4

Now in order for this table to have "real" numbers we must determine which variable requires the calculation of a constant.

Could the people who formulated this question think of a ny stupider way to ask it ?????
I'd stick around but I have to get away for a few hours. (remember to find the correct "constant" to see how much real time that is).