Answer:
The half life of a material is the time that a given quantity A of the material, decays into its half.
We know that the half-life is 4 hours, then we have the equation:
Q(t) = A*r^t
Where A is the initial quantity, and t is the number of hours.
and we have that r^4 = 1/2 (so when t = 4, we will have half of A)
then r = (1/2)^(1/4) = 0.84
Then our relation is
Q(t) = A*0.84^t
We have that A = 225mg,
at 1:00 pm. we have one hour after noon, so here we need to use t = 1.
Q(1) = 225mg*0.84^1 = 189.2mg
At 7:00 pm, we have 7 hours since noon, so here we need to use t = 7
Q(7) = 225mg*0.84^7 = 66.4mg
The equation is
[tex]Q(t) = A\times r^t[/tex]
here A is the initial quantity, and t is the number of hours.
Now
we have that r^4 = 1/2 (so when t = 4, we will have half of A)
So,
[tex]r = (1/2)^{(1/4)} = 0.84[/tex]
So, our relation is
[tex]Q(t) = A\times 0.84^t[/tex]
We have that A = 225mg,
Now
[tex]Q(1) = 225mg\times 0.84^1[/tex]= 189.2mg
And,
At 7:00 pm, we have 7 hours since noon, so here we need to use t = 7
[tex]Q(7) = 225mg\times 0.84^{7}[/tex] = 66.4mg
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