To solve this problem, we need to use the formula for exponential decay which is:

N = N0 * (1/2)^(t/T)

where:
N is the final amount of the substance,
N0 is the initial amount of the substance,
t is the time that has passed, and
T is the half-life of the substance.

In this case, we want to find N/N0, the fraction of Cobalt-60 left after 20.3 years. We know that T = 5.26 years.

So, we substitute these values into the formula:

N/N0 = (1/2)^(20.3/5.26)

Calculating the exponent first:

20.3/5.26 ≈ 3.86

Then, calculate the power:

(1/2)^3.86 ≈ 0.071

So, N/N0 ≈ 0.071

To express this as a percentage, we multiply by 100:

0.071 * 100 = 7.1%

So, approximately 7.1% of the Cobalt-60 would be left after 20.3 years.

Question

To solve this problem, we need to use the formula for exponential decay which is:

N = N0 * (1/2)^(t/T)

where:
N is the final amount of the substance,
N0 is the initial amount of the substance,
t is the time that has passed, and
T is the half-life of the substance.

In this case, we want to find N/N0, the fraction of Cobalt-60 left after 20.3 years. We know that T = 5.26 years.

So, we substitute these values into the formula:

N/N0 = (1/2)^(20.3/5.26)

Calculating the exponent first:

20.3/5.26 ≈ 3.86

Then, calculate the power:

(1/2)^3.86 ≈ 0.071

So, N/N0 ≈ 0.071

To express this as a percentage, we multiply by 100:

0.071 * 100 = 7.1%

So, approximately 7.1% of the Cobalt-60 would be left after 20.3 years.

Knowee AI · Accepted Answer