Question

The amount A, in grams, of a certain radioactive substance that remains after t years is given by A(t)=A0e−.06t, where A0 is the initial amount of the substance at t = 0. If A0=140 grams , approximately how much of the substance will remain after 5 years?

Answer 1

To find the remaining amount of a radioactive substance after 5 years with an initial amount of 140 grams, we use the formula A(t) = 140e^(-.06t) to calculate, resulting in approximately 103.7 grams remaining.

Step-by-step explanation:

The amount of a certain radioactive substance remaining after a period of time can be determined using the initial amount of the substance and the rate of decay. The given formula A(t) = A0e−.06t represents the exponential decay of a radioactive substance, where A0 is the initial amount and the decay rate is 0.06 per year. To find out how much of the substance will remain after 5 years with an initial amount of 140 grams, we plug in the values to get A(5) = 140e−(.06)(5).

First, calculate the exponent, which is −(.06)(5) = −0.3. Then, calculate e to the power of −0.3. The result is approximately e−0.3 ≈ 0.7408. Finally, multiply this by 140 grams to find the remaining amount, which is approximately 140 × 0.7408 ≈ 103.712 grams.

Therefore, after 5 years, approximately 103.7 grams of the radioactive substance will remain.