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?

Question

campbell_st · Answer

ok.. this is exponential growth and decay

is the model you are using similar to 

$$A = A_{0}e^{-kt}$$

A0 is the initial quantity t = time and k = decay constant...?

campbell_st · Answer

is that the model..?

anonymous · Answer

i guess i honestly dont know

anonymous · Answer

i know it has something to do with arthmetic

campbell_st · Answer

well the solution will require logarithms... do you understand them..?

anonymous · Answer

ya sort of and this question is under the topic of Geometric Sequences

anonymous · Answer

The nth term of a geometric sequence has the form:

an = a1r n-1

Where r is the common ratio of consecutive terms of the sequence.

campbell_st · Answer

ok... so you know a = 1 and $$a_{5} = 0.5$$ and t = 5

so you need to find r the common ratio.. 

$$0.5 = 1 \times r^{5 -1}$$

so 

$$r = \sqrt[5]{0.5}$$

I'd expect you will need to evaluate r. 

then you can find t

$$1 = 32r^{t - 1}$$

which will require logs to solve for t