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.

Question

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.

P.S. the 0 is at the bottom of the A nit at the top exponent . And the -kt is an exponent to e.

Answer 1

huh. They gave you the formula, as well as the numbers. Just evaluate

1000 e^(-.028*50)

Answer 2

To find out how much of 1,000 mg of strontium 90 remains after 50 years using the given equation A = A^0 * e^(-kt), where A^0 is the initial amount, A is the amount after t years, and k is the decay constant (0.028 for strontium 90), follow these steps:

Step 1: Plug in the values into the equation.
A = 1000 * e^(-0.028 * 50)

Step 2: Simplify the equation.
A = 1000 * e^(-1.4)

Step 3: Use a calculator or a mathematical software to calculate e^(-1.4).
e^(-1.4) ≈ 0.2466

Step 4: Multiply the initial amount (1000 mg) by the value obtained in the previous step.
A ≈ 1000 * 0.2466
A ≈ 246.6

Therefore, approximately 246.6 mg of strontium 90 remains after 50 years. Remember to round your answer to four decimal places, so the final answer would be 246.6000 mg.