Can someone please help me with this?
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If the radio active isotope has the half life of 24100 years, then the initial quantity is 2.16 grams
The half life in years = 24100
Consider the quantity of the radio active isotope remaining
y =
When t = 1000 the y = 1.2
y = C/2 when t = 1599
Substitute the values in the equation
C/2 =
Cancel the C in both side
1/2 =
Here we have to apply ln to eliminate the e terms
ln (1/2) = 24100k
k = ln(1/2) / 24100
k = -2.87× 10^-5
To find the initial value we have to substitute the value of k and y in the equation
1.2 = Ce^{1000 × -2.87× 10^-5}
C = 1.2 / e^(-0.0287)
C = 2.16 gram
Hence, the initial quantity of the radioactive isotope is 2.16 gram
Learn more about half life here
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we are given
system of equations
First equation is
Second equation is
now, we can find augmented matrix
now, we can change it into reduced row echelon form
step-1: multiply the 1st row by 1/3
step-2:add -3 times the 1st row to the 2nd row
step-3:multiply the 2nd row by 1/4
step-4: add 2/3 times the 2nd row to the 1st row
so, we get
Answer is (5,-8)