Question

The half-life of radium-224 is approximately 3.66 days. Step 1 of 3 : Determine a so that A(t)=A0at describes the amount of radium-224 left after t days, where A0 is the amount at time t=0. Round to six decimal places.

Answer 1

Answer:

a = 0.827468

Explanation:

given,

half life of radium-224 = 3.66 days

now,

 $A(t) = A_0 a^t$

t is the time

A₀ is the amount at t = 0

at t = 0 ,    A(0) = 1

A(3.66) = 1/2

at t = 3.66

$A(t) = A_0 a^t$

$\dfrac{1}{2}= 1. a^{3.66}$

taking log both side

3.66 log (a) = log (0.5)

       log a = -0.0822

now,$a = 10^{-0.0822}$

         a = 0.827468