SOLUTION: Given 100 grams of a substance that decays in accordance with the equation below, what is the half life? A(t)= (100)(.98)^t

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Given 100 grams of a substance that decays in accordance with the equation below, what is the half life? A(t)= (100)(.98)^t       Log On


   

Question 932843: Given 100 grams of a substance that decays in accordance with the equation below, what is the half life?
A(t)= (100)(.98)^t
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Half-life for HALF the quantity of the original quantity.

1%2F2=1%2A%280.98%29%5Et

What base do you want to use? Common logs for base 10?

log%2810%281%2F2%29%29=t%2Alog%2810%2C0.98%29

t=log%2810%2C%281%2F2%29%29%2Flog%2810%2C0.98%29

t=0.30103%2F0.00877

highlight_green%28t=34.34%29 years.


A quick check (?),
50=100%2A%280.98%29%5E34.3 ?
Okay!