Using the decay rate equation (N=No*e(-λ*t)) Calculate the original amount of material if the amount you have left after 150 years is 432.139 g if the decay constant of the material is 0.00027 g/year. Show all work
To calculate the original amount of material (No) using the decay rate equation N = No * e^(-λ * t), we can substitute the given values and solve for No.
Given values:
N = 432.139 g (amount remaining after 150 years)
λ = 0.00027 g/year (decay constant)
t = 150 years (time)
Step 1: Substitute the given values into the decay rate equation.
432.139 g = No * e^(-0.00027 g/year * 150 years)
Step 2: Simplify the equation by evaluating the exponential term.
432.139 g = No * e^(-0.0405)
Step 3: Solve for No by dividing both sides of the equation by e^(-0.0405).
No = 432.139 g / e^(-0.0405)
Step 4: Calculate the value of e^(-0.0405) using a calculator.
e^(-0.0405) ≈ 0.960769
Step 5: Substitute the calculated value into the equation.
No = 432.139 g / 0.960769
Step 6: Divide to find the value of No.
No ≈ 449.856 g
Therefore, the original amount of material is approximately 449.856 g.