HALF LIFE PROBLEM... PLZ HELP

[stezza]

PREDICT THE TIME WHEN HALF THE M&M'S WOULD BE LEFT USING HALF LIFE. THE INFORMATIONS WE HAVE IS THAT WE STARTED WITH 185 M&M'S. HOW CAN I PUT THIS INTO THE HALF LIFE EQUATION AND SOLVE IT?

 

[mmm4444bot]

Mmmm, a tasty exercise.

I regret that I do not know the half-life of an M&M. (I think it depends upon whether or not my sister is in the vicinity.)

Seriously, though, there is not enough information given to finish this exercise.

Are you sure that you provided us ALL of the given information ?

Also, please show us what you were given for the general "half-life equation".

 

[stezza]

Re:

Mmmm, a tasty exercise.

I regret that I do not know the half-life of an M&M. (I think it depends upon whether or not my sister is in the vicinity.)

Seriously, though, there is not enough information given to finish this exercise.

Are you sure that you provided us ALL of the given information ?

Also, please show us what you were given for the general "half-life equation".

we were not given an equation we had to google the equation. we had to set up a table and record the data of m&m's that had the m showing or not and use that information to produce the half life. our results were

X Y^m Y^Nom
1 99 86
2 29 57
3 35 24
4 9 15
5 5 10
6 4 4
7 4 2
8 1 1


x being number of trials

we were told ot use y^Nom information

i have put it in an equation 1= 185 x (0.5)^t/92.5

but how do i solve the equation for t?

 

[mmm4444bot]

record the data of m&m's that had the m showing or not and use that information to produce the half life This is weird.



i have put it in an equation 1 = 185 x (0.5)^(t/92.5) ? We need to type parentheses around fractional exponents.

Okay. This equation shows that the half-life of an M&M is 92.5 units of time.

By the way, what is the time unit ? Does t represent elapsed time in seconds ? In other words, is 92.5 seconds the half-life of an M&M ?

1 = 185(0.5)^(t/92.5)

Since the variable appears as part of the exponent, we need to use logarithms.

Before taking some logarithm of each side, first isolate the power of 0.5. In other words, divide both sides by 185.

1/185 = (0.5)^(t/92.5)

Now take a logarithm of both sides (I'll use the naturally-based logarithm). Then, apply the famous property that allows us to move the exponent "down in front".

ln(1/185) = ln([0.5]^[t/92.5])

ln(1/185) = (t/92.5) ln(0.5)

Can you finish solving for t now ?

I get the following approximation (assuming the time units to be seconds):

It takes about 696.65 seconds for 185 M&Ms to decay such that there's only one left.