SOLUTION: How do I solve the following: An initial quantity of material 'X' has decayed to 2000mg after 6 hrs and 1200mg after 10hrs. What was the initial mass of material 'X' and how muc

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve the following: An initial quantity of material 'X' has decayed to 2000mg after 6 hrs and 1200mg after 10hrs. What was the initial mass of material 'X' and how muc      Log On


   

Question 396425: How do I solve the following:
An initial quantity of material 'X' has decayed to 2000mg after 6 hrs and 1200mg after 10hrs. What was the initial mass of material 'X' and how much would remain after 22hrs.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An initial quantity of material 'X' has decayed to 2000mg after 6 hrs and 1200mg after 10hrs.
What was the initial mass of material 'X' and how much would remain after 22hrs.
:
assign the values as follows; x=time in hrs, y=amt of material
x1=6; y1=2000;
x2=10; y2=1200
Find the slope: m = %281200-2000%29%2F%2810-6%29 = %28-800%29%2F4 = -200
:
Use the point slope formula
y - 2000 = -200(x - 6)
y - 2000 = -200x + 1200
y = -200x + 1200 + 2000
y = -200x + 3200
:
Initial amt occurs when x = 0
y = 3200 is the initial amt
:
Use this amt in the decay formula
we will use a half life of 8 hrs, (1600 is half way between 6 and 10 hr amts)
A = Ao*2^(-t/h)
A = 3200*2^(-t/8}
:
Here is a graph of the two formulas

hr 6 and hr 10 are close
:
Use the decay formula to find amt after 22 days
A = 3200*2^(-22/8}
A = 476 mg after 22 hrs