SOLUTION: The half life of Iron-55 is approximately 2.7 years. Determine a so that A(t)=Aoa^t describes the amount of iron-55 left after t years where Ao is the amount at time t=0. Round

Algebra ->  Functions -> SOLUTION: The half life of Iron-55 is approximately 2.7 years. Determine a so that A(t)=Aoa^t describes the amount of iron-55 left after t years where Ao is the amount at time t=0. Round       Log On


   

Question 923481: The half life of Iron-55 is approximately 2.7 years.
Determine a so that A(t)=Aoa^t describes the amount of iron-55 left after t years where Ao is the amount at time t=0. Round to 6 decimal places.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Using common logs and A(2.7)=1/2 and A(0)=1,

highlight_green%281%2F2=1%2Aa%5E%282.7%29%29

log%28%281%2F2%29%29=log%28%28a%5E%282.7%29%29%29

log%28%281%2F2%29%29=2.7%2Alog%28%28a%29%29

log%28%28a%29%29=log%28%281%2F2%29%29%2F2.7

log%28%28a%29%29=-%280.30103%29%2F%282.7%29

highlight_green%28log%28%28a%29%29=-0.11149%29

highlight%28a=0.773584%29 based on 10%5E%28-0.111493%29.