SOLUTION: I hope someone can explain where I went wrong????? The chemical element strontium has a half-life of 25 years. If 32g were present initially, how long will it take for the amoun

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I hope someone can explain where I went wrong????? The chemical element strontium has a half-life of 25 years. If 32g were present initially, how long will it take for the amoun      Log On


   

Question 185081: I hope someone can explain where I went wrong?????
The chemical element strontium has a half-life of 25 years. If 32g were present initially, how long will it take for the amount to be reduced to 2g? Set up an exponential equation and solve algebraically.
This is what I did:
y=32(1/2)^x/25
2=32(1/2)^x/25
2/32=1/2^x/25
1/16=1/2^x/5
Then I finished it using logs but my teacher said that I was supposed to solve it algebraically !!??!?!? HOW?
This is how I finished it:
(log(1/16)/ log(1/2))=(log(1/2)^x/5)/(log(1/2))
4=x/5
20=x
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

You have done everything right. It is just that when you got to the point of saying:



You might have noticed that:



From which you could then deduce that:



I think you should be able to take it from there.

The answer you got by using logs would have been correct if you had not, for some inexplicable reason, changed the half-life number from 25 to 5 in the denominator of your fractional exponent.

John