The radioactive decay of a substance is expressed by A=A^0 e^ -kt, where the initial amount A^0, decays to an amount A after t years. The positive constant k differs for each substance. Strontium 90 decays such that k=.028. Find out how much of 1,000 mg of strontium 90 remains after 50 years. Round your answer to four decimal places
-The 0 is at the bottom of the A and the -kt is an exponent to e
well, you have the equation. Just plug in
Ao = 1000
t = 50
To find out how much of the 1,000 mg of Strontium 90 remains after 50 years, we can use the given formula:
A = A^0 * e^(-kt)
First, let's substitute the known values into the equation. We have A^0 = 1,000 mg and k = 0.028.
A = 1,000 mg * e^(-0.028 * 50)
Now we can simplify the equation by calculating the exponent term inside the exponential function.
A = 1,000 mg * e^(-1.4)
To get the final answer, we need to evaluate the exponential term e^(-1.4). You can do this using a scientific calculator or an online calculator that provides the exponential function.
After evaluating e^(-1.4), we find that approximately 0.2466 remains.
Therefore, after 50 years, approximately 246.6 mg (rounded to four decimal places) of the initial 1,000 mg of Strontium 90 will remain.